CINXE.COM

<!DOCTYPE html> <html lang="en" dir="ltr"> <head>  <script async src="https://www.googletagmanager.com/gtag/js?id=G-P63WKM1TM1"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-P63WKM1TM1'); </script>  <script type="text/javascript" > (function(m,e,t,r,i,k,a){m[i]=m[i]||function(){(m[i].a=m[i].a||[]).push(arguments)}; m[i].l=1*new Date(); for (var j = 0; j < document.scripts.length; j++) {if (document.scripts[j].src === r) { return; }} k=e.createElement(t),a=e.getElementsByTagName(t)[0],k.async=1,k.src=r,a.parentNode.insertBefore(k,a)}) (window, document, "script", "https://mc.yandex.ru/metrika/tag.js", "ym"); ym(55165297, "init", { clickmap:false, trackLinks:true, accurateTrackBounce:true, webvisor:false }); </script> <noscript><div><img src="https://mc.yandex.ru/watch/55165297" style="position:absolute; left:-9999px;" alt="" /></div></noscript>    <title>Search results for: convex optimization</title> <meta name="description" content="Search results for: convex optimization"> <meta name="keywords" content="convex optimization"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block d-lg-none navbar-toggler ml-auto" type="button" data-toggle="collapse" data-target="#navbarMenu" aria-controls="navbarMenu" aria-expanded="false" aria-label="Toggle navigation"> <span class="navbar-toggler-icon"></span> </button> <div class="w-100"> <div class="d-none d-lg-flex flex-row-reverse"> <form method="get" action="https://waset.org/search" class="form-inline my-2 my-lg-0"> <input class="form-control mr-sm-2" type="search" placeholder="Search Conferences" value="convex optimization" name="q" aria-label="Search"> <button class="btn btn-light my-2 my-sm-0" type="submit"><i class="fas fa-search"></i></button> </form> </div> <div class="collapse navbar-collapse mt-1" id="navbarMenu"> <ul class="navbar-nav ml-auto align-items-center" id="mainNavMenu"> <li class="nav-item"> <a class="nav-link" href="https://waset.org/conferences" title="Conferences in 2024/2025/2026">Conferences</a> </li> <li class="nav-item"> <a class="nav-link" href="https://waset.org/disciplines" title="Disciplines">Disciplines</a> </li> <li class="nav-item"> <a class="nav-link" href="https://waset.org/committees" rel="nofollow">Committees</a> </li> <li class="nav-item dropdown"> <a class="nav-link dropdown-toggle" href="#" id="navbarDropdownPublications" role="button" data-toggle="dropdown" aria-haspopup="true" aria-expanded="false"> Publications </a> <div class="dropdown-menu" aria-labelledby="navbarDropdownPublications"> <a class="dropdown-item" href="https://publications.waset.org/abstracts">Abstracts</a> <a class="dropdown-item" href="https://publications.waset.org">Periodicals</a> <a class="dropdown-item" href="https://publications.waset.org/archive">Archive</a> </div> </li> <li class="nav-item"> <a class="nav-link" href="https://waset.org/page/support" title="Support">Support</a> </li> </ul> </div> </div> </nav> </div> </header> <main> <div class="container mt-4"> <div class="row"> <div class="col-md-9 mx-auto"> <form method="get" action="https://publications.waset.org/abstracts/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="convex optimization"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 3327</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: convex optimization</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3327</span> Approximation of Convex Set by Compactly Semidefinite Representable Set</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Anusuya%20Ghosh">Anusuya Ghosh</a>, <a href="https://publications.waset.org/abstracts/search?q=Vishnu%20Narayanan"> Vishnu Narayanan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The approximation of convex set by semidefinite representable set plays an important role in semidefinite programming, especially in modern convex optimization. To optimize a linear function over a convex set is a hard problem. But optimizing the linear function over the semidefinite representable set which approximates the convex set is easy to solve as there exists numerous efficient algorithms to solve semidefinite programming problems. So, our approximation technique is significant in optimization. We develop a technique to approximate any closed convex set, say K by compactly semidefinite representable set. Further we prove that there exists a sequence of compactly semidefinite representable sets which give tighter approximation of the closed convex set, K gradually. We discuss about the convergence of the sequence of compactly semidefinite representable sets to closed convex set K. The recession cone of K and the recession cone of the compactly semidefinite representable set are equal. So, we say that the sequence of compactly semidefinite representable sets converge strongly to the closed convex set. Thus, this approximation technique is very useful development in semidefinite programming. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=semidefinite%20programming" title="semidefinite programming">semidefinite programming</a>, <a href="https://publications.waset.org/abstracts/search?q=semidefinite%20representable%20set" title=" semidefinite representable set"> semidefinite representable set</a>, <a href="https://publications.waset.org/abstracts/search?q=compactly%20semidefinite%20representable%20set" title=" compactly semidefinite representable set"> compactly semidefinite representable set</a>, <a href="https://publications.waset.org/abstracts/search?q=approximation" title=" approximation"> approximation</a> </p> <a href="https://publications.waset.org/abstracts/36914/approximation-of-convex-set-by-compactly-semidefinite-representable-set" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/36914.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">386</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3326</span> From Convexity in Graphs to Polynomial Rings</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ladznar%20S.%20Laja">Ladznar S. Laja</a>, <a href="https://publications.waset.org/abstracts/search?q=Rosalio%20G.%20Artes"> Rosalio G. Artes</a>, <a href="https://publications.waset.org/abstracts/search?q=Jr."> Jr.</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper introduced a graph polynomial relating convexity concepts. A graph polynomial is a polynomial representing a graph given some parameters. On the other hand, a subgraph H of a graph G is said to be convex in G if for every pair of vertices in H, every shortest path with these end-vertices lies entirely in H. We define the convex subgraph polynomial of a graph G to be the generating function of the sequence of the numbers of convex subgraphs of G of cardinalities ranging from zero to the order of G. This graph polynomial is monic since G itself is convex. The convex index which counts the number of convex subgraphs of G of all orders is just the evaluation of this polynomial at 1. Relationships relating algebraic properties of convex subgraphs polynomial with graph theoretic concepts are established. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=convex%20subgraph" title="convex subgraph">convex subgraph</a>, <a href="https://publications.waset.org/abstracts/search?q=convex%20index" title=" convex index"> convex index</a>, <a href="https://publications.waset.org/abstracts/search?q=generating%20function" title=" generating function"> generating function</a>, <a href="https://publications.waset.org/abstracts/search?q=polynomial%20ring" title=" polynomial ring"> polynomial ring</a> </p> <a href="https://publications.waset.org/abstracts/9019/from-convexity-in-graphs-to-polynomial-rings" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/9019.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">215</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3325</span> Jensen's Inequality and M-Convex Functions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yamin%20Sayyari">Yamin Sayyari</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we generalized the Jensen's inequality for m-convex functions and also we present a correction of Jensen's inequality which is a better than the generalization of this inequality for m-convex functions. Finally, we have found new lower and new upper bounds for Jensen's discrete inequality. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jensen%27s%20inequality" title="Jensen's inequality">Jensen's inequality</a>, <a href="https://publications.waset.org/abstracts/search?q=m-convex%20function" title=" m-convex function"> m-convex function</a>, <a href="https://publications.waset.org/abstracts/search?q=Convex%20function" title=" Convex function"> Convex function</a>, <a href="https://publications.waset.org/abstracts/search?q=Inequality" title=" Inequality"> Inequality</a> </p> <a href="https://publications.waset.org/abstracts/129556/jensens-inequality-and-m-convex-functions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/129556.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">144</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3324</span> Estimating View-Through Ad Attribution from User Surveys Using Convex Optimization</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yuhan%20Lin">Yuhan Lin</a>, <a href="https://publications.waset.org/abstracts/search?q=Rohan%20Kekatpure"> Rohan Kekatpure</a>, <a href="https://publications.waset.org/abstracts/search?q=Cassidy%20Yeung"> Cassidy Yeung</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In Digital Marketing, robust quantification of View-through attribution (VTA) is necessary for evaluating channel effectiveness. VTA occurs when a product purchase is aided by an Ad but without an explicit click (e.g. a TV ad). A lack of a tracking mechanism makes VTA estimation challenging. Most prevalent VTA estimation techniques rely on post-purchase in-product user surveys. User surveys enable the calculation of channel multipliers, which are the ratio of the view-attributed to the click-attributed purchases of each marketing channel. Channel multipliers thus provide a way to estimate the unknown VTA for a channel from its known click attribution. In this work, we use Convex Optimization to compute channel multipliers in a way that enables a mathematical encoding of the expected channel behavior. Large fluctuations in channel attributions often result from overfitting the calculations to user surveys. Casting channel attribution as a Convex Optimization problem allows an introduction of constraints that limit such fluctuations. The result of our study is a distribution of channel multipliers across the entire marketing funnel, with important implications for marketing spend optimization. Our technique can be broadly applied to estimate Ad effectiveness in a privacy-centric world that increasingly limits user tracking. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=digital%20marketing" title="digital marketing">digital marketing</a>, <a href="https://publications.waset.org/abstracts/search?q=survey%20analysis" title=" survey analysis"> survey analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=operational%20research" title=" operational research"> operational research</a>, <a href="https://publications.waset.org/abstracts/search?q=convex%20optimization" title=" convex optimization"> convex optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=channel%20attribution" title=" channel attribution"> channel attribution</a> </p> <a href="https://publications.waset.org/abstracts/149140/estimating-view-through-ad-attribution-from-user-surveys-using-convex-optimization" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/149140.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">199</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3323</span> Sparse-View CT Reconstruction Based on Nonconvex L1 − L2 Regularizations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ali%20Pour%20Yazdanpanah">Ali Pour Yazdanpanah</a>, <a href="https://publications.waset.org/abstracts/search?q=Farideh%20Foroozandeh%20Shahraki"> Farideh Foroozandeh Shahraki</a>, <a href="https://publications.waset.org/abstracts/search?q=Emma%20Regentova"> Emma Regentova</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The reconstruction from sparse-view projections is one of important problems in computed tomography (CT) limited by the availability or feasibility of obtaining of a large number of projections. Traditionally, convex regularizers have been exploited to improve the reconstruction quality in sparse-view CT, and the convex constraint in those problems leads to an easy optimization process. However, convex regularizers often result in a biased approximation and inaccurate reconstruction in CT problems. Here, we present a nonconvex, Lipschitz continuous and non-smooth regularization model. The CT reconstruction is formulated as a nonconvex constrained L1 − L2 minimization problem and solved through a difference of convex algorithm and alternating direction of multiplier method which generates a better result than L0 or L1 regularizers in the CT reconstruction. We compare our method with previously reported high performance methods which use convex regularizers such as TV, wavelet, curvelet, and curvelet+TV (CTV) on the test phantom images. The results show that there are benefits in using the nonconvex regularizer in the sparse-view CT reconstruction. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=computed%20tomography" title="computed tomography">computed tomography</a>, <a href="https://publications.waset.org/abstracts/search?q=non-convex" title=" non-convex"> non-convex</a>, <a href="https://publications.waset.org/abstracts/search?q=sparse-view%20reconstruction" title=" sparse-view reconstruction"> sparse-view reconstruction</a>, <a href="https://publications.waset.org/abstracts/search?q=L1-L2%20minimization" title=" L1-L2 minimization"> L1-L2 minimization</a>, <a href="https://publications.waset.org/abstracts/search?q=difference%20of%20convex%20functions" title=" difference of convex functions"> difference of convex functions</a> </p> <a href="https://publications.waset.org/abstracts/70473/sparse-view-ct-reconstruction-based-on-nonconvex-l1-l2-regularizations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/70473.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">316</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3322</span> Optimality Conditions for Weak Efficient Solutions Generated by a Set Q in Vector Spaces</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Elham%20Kiyani">Elham Kiyani</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Mansour%20Vaezpour"> S. Mansour Vaezpour</a>, <a href="https://publications.waset.org/abstracts/search?q=Javad%20Tavakoli"> Javad Tavakoli</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we first introduce a new distance function in a linear space not necessarily endowed with a topology. The algebraic concepts of interior and closure are useful to study optimization problems without topology. So, we define Q-weak efficient solutions generated by the algebraic interior of a set Q, where Q is not necessarily convex. Studying nonconvex vector optimization is valuable since, for a convex cone K in topological spaces, we have int(K)=cor(K), which means that topological interior of a convex cone K is equal to the algebraic interior of K. Moreover, we used the scalarization technique including the distance function generated by the vectorial closure of a set to characterize these Q-weak efficient solutions. Scalarization is a useful approach for solving vector optimization problems. This technique reduces the optimization problem to a scalar problem which tends to be an optimization problem with a real-valued objective function. For instance, Q-weak efficient solutions of vector optimization problems can be characterized and computed as solutions of appropriate scalar optimization problems. In the convex case, linear functionals can be used as objective functionals of the scalar problems. But in the nonconvex case, we should present a suitable objective function. It is the aim of this paper to present a new distance function that be useful to obtain sufficient and necessary conditions for Q-weak efficient solutions of general optimization problems via scalarization. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=weak%20efficient" title="weak efficient">weak efficient</a>, <a href="https://publications.waset.org/abstracts/search?q=algebraic%20interior" title=" algebraic interior"> algebraic interior</a>, <a href="https://publications.waset.org/abstracts/search?q=vector%20closure" title=" vector closure"> vector closure</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20space" title=" linear space"> linear space</a> </p> <a href="https://publications.waset.org/abstracts/94737/optimality-conditions-for-weak-efficient-solutions-generated-by-a-set-q-in-vector-spaces" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/94737.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">228</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3321</span> Subclass of Close-To-Convex Harmonic Mappings</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jugal%20K.%20Prajapat">Jugal K. Prajapat</a>, <a href="https://publications.waset.org/abstracts/search?q=Manivannan%20M."> Manivannan M.</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this article we have studied a class of sense preserving harmonic mappings in the unit disk D. Let B⁰H (α, β) denote the class of sense-preserving harmonic mappings f=h+g ̅ in the open unit disk D and satisfying the condition |z h״(z)+α (h׳(z)-1) | ≤ β - |z g″(z)+α g′(z)| (α > -1, β > 0). We have proved that B⁰H (α, β) is close-to-convex in D. We also prove that the functions in B⁰H (α, β) are stable harmonic univalent, stable harmonic starlike and stable harmonic convex in D for different values of its parameters. Further, the coefficient estimates, growth results, area theorem, boundary behavior, convolution and convex combination properties of the class B⁰H (α, β) of harmonic mapping are obtained. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=analytic" title="analytic">analytic</a>, <a href="https://publications.waset.org/abstracts/search?q=univalent" title=" univalent"> univalent</a>, <a href="https://publications.waset.org/abstracts/search?q=starlike" title=" starlike"> starlike</a>, <a href="https://publications.waset.org/abstracts/search?q=convex%20and%20close-to-convex" title=" convex and close-to-convex"> convex and close-to-convex</a> </p> <a href="https://publications.waset.org/abstracts/109786/subclass-of-close-to-convex-harmonic-mappings" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/109786.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">175</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3320</span> Non-Convex Multi Objective Economic Dispatch Using Ramp Rate Biogeography Based Optimization</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Susanta%20Kumar%20Gachhayat">Susanta Kumar Gachhayat</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20K.%20Dash"> S. K. Dash</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Multi objective non-convex economic dispatch problems of a thermal power plant are of grave concern for deciding the cost of generation and reduction of emission level for diminishing the global warming level for improving green-house effect. This paper deals with ramp rate constraints for achieving better inequality constraints so as to incorporate valve point loading for cost of generation in thermal power plant through ramp rate biogeography based optimization involving mutation and migration. Through 50 out of 100 trials, the cost function and emission objective function were found to have outperformed other classical methods such as lambda iteration method, quadratic programming method and many heuristic methods like particle swarm optimization method, weight improved particle swarm optimization method, constriction factor based particle swarm optimization method, moderate random particle swarm optimization method etc. Ramp rate biogeography based optimization applications prove quite advantageous in solving non convex multi objective economic dispatch problems subjected to nonlinear loads that pollute the source giving rise to third harmonic distortions and other such disturbances. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=economic%20load%20dispatch" title="economic load dispatch">economic load dispatch</a>, <a href="https://publications.waset.org/abstracts/search?q=ELD" title=" ELD"> ELD</a>, <a href="https://publications.waset.org/abstracts/search?q=biogeography-based%20optimization" title=" biogeography-based optimization"> biogeography-based optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=BBO" title=" BBO"> BBO</a>, <a href="https://publications.waset.org/abstracts/search?q=ramp%20rate%20biogeography-based%20optimization" title=" ramp rate biogeography-based optimization"> ramp rate biogeography-based optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=RRBBO" title=" RRBBO"> RRBBO</a>, <a href="https://publications.waset.org/abstracts/search?q=valve-point%20loading" title=" valve-point loading"> valve-point loading</a>, <a href="https://publications.waset.org/abstracts/search?q=VPL" title=" VPL"> VPL</a> </p> <a href="https://publications.waset.org/abstracts/67748/non-convex-multi-objective-economic-dispatch-using-ramp-rate-biogeography-based-optimization" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/67748.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">379</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3319</span> Q-Efficient Solutions of Vector Optimization via Algebraic Concepts</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Elham%20Kiyani">Elham Kiyani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we first introduce the concept of Q-efficient solutions in a real linear space not necessarily endowed with a topology, where Q is some nonempty (not necessarily convex) set. We also used the scalarization technique including the Gerstewitz function generated by a nonconvex set to characterize these Q-efficient solutions. The algebraic concepts of interior and closure are useful to study optimization problems without topology. Studying nonconvex vector optimization is valuable since topological interior is equal to algebraic interior for a convex cone. So, we use the algebraic concepts of interior and closure to define Q-weak efficient solutions and Q-Henig proper efficient solutions of set-valued optimization problems, where Q is not a convex cone. Optimization problems with set-valued maps have a wide range of applications, so it is expected that there will be a useful analytical tool in optimization theory for set-valued maps. These kind of optimization problems are closely related to stochastic programming, control theory, and economic theory. The paper focus on nonconvex problems, the results are obtained by assuming generalized non-convexity assumptions on the data of the problem. In convex problems, main mathematical tools are convex separation theorems, alternative theorems, and algebraic counterparts of some usual topological concepts, while in nonconvex problems, we need a nonconvex separation function. Thus, we consider the Gerstewitz function generated by a general set in a real linear space and re-examine its properties in the more general setting. A useful approach for solving a vector problem is to reduce it to a scalar problem. In general, scalarization means the replacement of a vector optimization problem by a suitable scalar problem which tends to be an optimization problem with a real valued objective function. The Gerstewitz function is well known and widely used in optimization as the basis of the scalarization. The essential properties of the Gerstewitz function, which are well known in the topological framework, are studied by using algebraic counterparts rather than the topological concepts of interior and closure. Therefore, properties of the Gerstewitz function, when it takes values just in a real linear space are studied, and we use it to characterize Q-efficient solutions of vector problems whose image space is not endowed with any particular topology. Therefore, we deal with a constrained vector optimization problem in a real linear space without assuming any topology, and also Q-weak efficient and Q-proper efficient solutions in the senses of Henig are defined. Moreover, by means of the Gerstewitz function, we provide some necessary and sufficient optimality conditions for set-valued vector optimization problems. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=algebraic%20interior" title="algebraic interior">algebraic interior</a>, <a href="https://publications.waset.org/abstracts/search?q=Gerstewitz%20function" title=" Gerstewitz function"> Gerstewitz function</a>, <a href="https://publications.waset.org/abstracts/search?q=vector%20closure" title=" vector closure"> vector closure</a>, <a href="https://publications.waset.org/abstracts/search?q=vector%20optimization" title=" vector optimization"> vector optimization</a> </p> <a href="https://publications.waset.org/abstracts/94011/q-efficient-solutions-of-vector-optimization-via-algebraic-concepts" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/94011.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">216</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3318</span> Generalized Central Paths for Convex Programming</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Li-Zhi%20Liao">Li-Zhi Liao</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The central path has played the key role in the interior point method. However, the convergence of the central path may not be true even in some convex programming problems with linear constraints. In this paper, the generalized central paths are introduced for convex programming. One advantage of the generalized central paths is that the paths will always converge to some optimal solutions of the convex programming problem for any initial interior point. Some additional theoretical properties for the generalized central paths will be also reported. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=central%20path" title="central path">central path</a>, <a href="https://publications.waset.org/abstracts/search?q=convex%20programming" title=" convex programming"> convex programming</a>, <a href="https://publications.waset.org/abstracts/search?q=generalized%20central%20path" title=" generalized central path"> generalized central path</a>, <a href="https://publications.waset.org/abstracts/search?q=interior%20point%20method" title=" interior point method"> interior point method</a> </p> <a href="https://publications.waset.org/abstracts/58039/generalized-central-paths-for-convex-programming" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/58039.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">327</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3317</span> Optrix: Energy Aware Cross Layer Routing Using Convex Optimization in Wireless Sensor Networks</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ali%20Shareef">Ali Shareef</a>, <a href="https://publications.waset.org/abstracts/search?q=Aliha%20Shareef"> Aliha Shareef</a>, <a href="https://publications.waset.org/abstracts/search?q=Yifeng%20Zhu"> Yifeng Zhu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Energy minimization is of great importance in wireless sensor networks in extending the battery lifetime. One of the key activities of nodes in a WSN is communication and the routing of their data to a centralized base-station or sink. Routing using the shortest path to the sink is not the best solution since it will cause nodes along this path to fail prematurely. We propose a cross-layer energy efficient routing protocol Optrix that utilizes a convex formulation to maximize the lifetime of the network as a whole. We further propose, Optrix-BW, a novel convex formulation with bandwidth constraint that allows the channel conditions to be accounted for in routing. By considering this key channel parameter we demonstrate that Optrix-BW is capable of congestion control. Optrix is implemented in TinyOS, and we demonstrate that a relatively large topology of 40 nodes can converge to within 91% of the optimal routing solution. We describe the pitfalls and issues related with utilizing a continuous form technique such as convex optimization with discrete packet based communication systems as found in WSNs. We propose a routing controller mechanism that allows for this transformation. We compare Optrix against the Collection Tree Protocol (CTP) and we found that Optrix performs better in terms of convergence to an optimal routing solution, for load balancing and network lifetime maximization than CTP. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=wireless%20sensor%20network" title="wireless sensor network">wireless sensor network</a>, <a href="https://publications.waset.org/abstracts/search?q=Energy%20Efficient%20Routing" title=" Energy Efficient Routing"> Energy Efficient Routing</a> </p> <a href="https://publications.waset.org/abstracts/17333/optrix-energy-aware-cross-layer-routing-using-convex-optimization-in-wireless-sensor-networks" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/17333.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">391</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3316</span> Strong Convergence of an Iterative Sequence in Real Banach Spaces with Kadec Klee Property</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Umar%20Yusuf%20Batsari">Umar Yusuf Batsari</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Let E be a uniformly smooth and uniformly convex real Banach space and C be a nonempty, closed and convex subset of E. Let $V= \{S_i : C\to C, ~i=1, 2, 3\cdots N\}$ be a convex set of relatively nonexpansive mappings containing identity. In this paper, an iterative sequence obtained from CQ algorithm was shown to have strongly converge to a point $\hat{x}$ which is a common fixed point of relatively nonexpansive mappings in V and also solve the system of equilibrium problems in E. The result improve some existing results in the literature. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=relatively%20nonexpansive%20mappings" title="relatively nonexpansive mappings">relatively nonexpansive mappings</a>, <a href="https://publications.waset.org/abstracts/search?q=strong%20convergence" title=" strong convergence"> strong convergence</a>, <a href="https://publications.waset.org/abstracts/search?q=equilibrium%20problems" title=" equilibrium problems"> equilibrium problems</a>, <a href="https://publications.waset.org/abstracts/search?q=uniformly%20smooth%20space" title=" uniformly smooth space"> uniformly smooth space</a>, <a href="https://publications.waset.org/abstracts/search?q=uniformly%20convex%20space" title=" uniformly convex space"> uniformly convex space</a>, <a href="https://publications.waset.org/abstracts/search?q=convex%20set" title=" convex set"> convex set</a>, <a href="https://publications.waset.org/abstracts/search?q=kadec%20klee%20property" title=" kadec klee property"> kadec klee property</a> </p> <a href="https://publications.waset.org/abstracts/21142/strong-convergence-of-an-iterative-sequence-in-real-banach-spaces-with-kadec-klee-property" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/21142.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">422</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3315</span> An Improved Lower Bound for Minimal-Area Convex Cover for Closed Unit Curves</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=S.%20Som-Am">S. Som-Am</a>, <a href="https://publications.waset.org/abstracts/search?q=B.%20Grechuk"> B. Grechuk</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Moser’s worm problem is the unsolved problem in geometry which asks for the minimal area of a convex region on the plane which can cover all curves of unit length, assuming that curves may be rotated and translated to fit inside the region. We study a version of this problem asking for a minimal convex cover for closed unit curves. By combining geometric methods with numerical box’s search algorithm, we show that any such cover should have an area at least 0.0975. This improves the best previous lower bound of 0.096694. In fact, we show that the minimal area of convex hull of circle, equilateral triangle, and rectangle of perimeter 1 is between 0.0975 and 0.09763. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Moser%E2%80%99s%20worm%20problem" title="Moser’s worm problem">Moser’s worm problem</a>, <a href="https://publications.waset.org/abstracts/search?q=closed%20arcs" title=" closed arcs"> closed arcs</a>, <a href="https://publications.waset.org/abstracts/search?q=convex%20cover" title=" convex cover"> convex cover</a>, <a href="https://publications.waset.org/abstracts/search?q=minimal-area%20cover" title=" minimal-area cover"> minimal-area cover</a> </p> <a href="https://publications.waset.org/abstracts/92526/an-improved-lower-bound-for-minimal-area-convex-cover-for-closed-unit-curves" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/92526.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">211</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3314</span> Neural Network in Fixed Time for Collision Detection between Two Convex Polyhedra</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Khouil">M. Khouil</a>, <a href="https://publications.waset.org/abstracts/search?q=N.%20Saber"> N. Saber</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Mestari"> M. Mestari</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a different architecture of a collision detection neural network (DCNN) is developed. This network, which has been particularly reviewed, has enabled us to solve with a new approach the problem of collision detection between two convex polyhedra in a fixed time (O (1) time). We used two types of neurons, linear and threshold logic, which simplified the actual implementation of all the networks proposed. The study of the collision detection is divided into two sections, the collision between a point and a polyhedron and then the collision between two convex polyhedra. The aim of this research is to determine through the AMAXNET network a mini maximum point in a fixed time, which allows us to detect the presence of a potential collision. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=collision%20identification" title="collision identification">collision identification</a>, <a href="https://publications.waset.org/abstracts/search?q=fixed%20time" title=" fixed time"> fixed time</a>, <a href="https://publications.waset.org/abstracts/search?q=convex%20polyhedra" title=" convex polyhedra"> convex polyhedra</a>, <a href="https://publications.waset.org/abstracts/search?q=neural%20network" title=" neural network"> neural network</a>, <a href="https://publications.waset.org/abstracts/search?q=AMAXNET" title=" AMAXNET"> AMAXNET</a> </p> <a href="https://publications.waset.org/abstracts/8931/neural-network-in-fixed-time-for-collision-detection-between-two-convex-polyhedra" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/8931.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">422</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3313</span> Comparative Analysis of Classical and Parallel Inpainting Algorithms Based on Affine Combinations of Projections on Convex Sets</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Irina%20Maria%20Artinescu">Irina Maria Artinescu</a>, <a href="https://publications.waset.org/abstracts/search?q=Costin%20Radu%20Boldea"> Costin Radu Boldea</a>, <a href="https://publications.waset.org/abstracts/search?q=Eduard-Ionut%20Matei"> Eduard-Ionut Matei</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The paper is a comparative study of two classical variants of parallel projection methods for solving the convex feasibility problem with their equivalents that involve variable weights in the construction of the solutions. We used a graphical representation of these methods for inpainting a convex area of an image in order to investigate their effectiveness in image reconstruction applications. We also presented a numerical analysis of the convergence of these four algorithms in terms of the average number of steps and execution time in classical CPU and, alternatively, in parallel GPU implementation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=convex%20feasibility%20problem" title="convex feasibility problem">convex feasibility problem</a>, <a href="https://publications.waset.org/abstracts/search?q=convergence%20analysis" title=" convergence analysis"> convergence analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=inpainting" title=" inpainting"> inpainting</a>, <a href="https://publications.waset.org/abstracts/search?q=parallel%20projection%20methods" title=" parallel projection methods"> parallel projection methods</a> </p> <a href="https://publications.waset.org/abstracts/133736/comparative-analysis-of-classical-and-parallel-inpainting-algorithms-based-on-affine-combinations-of-projections-on-convex-sets" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/133736.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">174</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3312</span> A Hybrid Particle Swarm Optimization-Nelder- Mead Algorithm (PSO-NM) for Nelson-Siegel- Svensson Calibration</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sofia%20Ayouche">Sofia Ayouche</a>, <a href="https://publications.waset.org/abstracts/search?q=Rachid%20Ellaia"> Rachid Ellaia</a>, <a href="https://publications.waset.org/abstracts/search?q=Rajae%20Aboulaich"> Rajae Aboulaich</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Today, insurers may use the yield curve as an indicator evaluation of the profit or the performance of their portfolios; therefore, they modeled it by one class of model that has the ability to fit and forecast the future term structure of interest rates. This class of model is the Nelson-Siegel-Svensson model. Unfortunately, many authors have reported a lot of difficulties when they want to calibrate the model because the optimization problem is not convex and has multiple local optima. In this context, we implement a hybrid Particle Swarm optimization and Nelder Mead algorithm in order to minimize by least squares method, the difference between the zero-coupon curve and the NSS curve. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=optimization" title="optimization">optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=zero-coupon%20curve" title=" zero-coupon curve"> zero-coupon curve</a>, <a href="https://publications.waset.org/abstracts/search?q=Nelson-Siegel-Svensson" title=" Nelson-Siegel-Svensson"> Nelson-Siegel-Svensson</a>, <a href="https://publications.waset.org/abstracts/search?q=particle%20swarm%20optimization" title=" particle swarm optimization"> particle swarm optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=Nelder-Mead%20algorithm" title=" Nelder-Mead algorithm"> Nelder-Mead algorithm</a> </p> <a href="https://publications.waset.org/abstracts/48619/a-hybrid-particle-swarm-optimization-nelder-mead-algorithm-pso-nm-for-nelson-siegel-svensson-calibration" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/48619.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">430</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3311</span> Finite-Sum Optimization: Adaptivity to Smoothness and Loopless Variance Reduction</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Bastien%20Batardi%C3%A8re">Bastien Batardière</a>, <a href="https://publications.waset.org/abstracts/search?q=Joon%20Kwon"> Joon Kwon</a> </p> <p class="card-text"><strong>Abstract:</strong></p> For finite-sum optimization, variance-reduced gradient methods (VR) compute at each iteration the gradient of a single function (or of a mini-batch), and yet achieve faster convergence than SGD thanks to a carefully crafted lower-variance stochastic gradient estimator that reuses past gradients. Another important line of research of the past decade in continuous optimization is the adaptive algorithms such as AdaGrad, that dynamically adjust the (possibly coordinate-wise) learning rate to past gradients and thereby adapt to the geometry of the objective function. Variants such as RMSprop and Adam demonstrate outstanding practical performance that have contributed to the success of deep learning. In this work, we present AdaLVR, which combines the AdaGrad algorithm with loopless variance-reduced gradient estimators such as SAGA or L-SVRG that benefits from a straightforward construction and a streamlined analysis. We assess that AdaLVR inherits both good convergence properties from VR methods and the adaptive nature of AdaGrad: in the case of L-smooth convex functions we establish a gradient complexity of O(n + (L + √ nL)/ε) without prior knowledge of L. Numerical experiments demonstrate the superiority of AdaLVR over state-of-the-art methods. Moreover, we empirically show that the RMSprop and Adam algorithm combined with variance-reduced gradients estimators achieve even faster convergence. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=convex%20optimization" title="convex optimization">convex optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=variance%20reduction" title=" variance reduction"> variance reduction</a>, <a href="https://publications.waset.org/abstracts/search?q=adaptive%20algorithms" title=" adaptive algorithms"> adaptive algorithms</a>, <a href="https://publications.waset.org/abstracts/search?q=loopless" title=" loopless"> loopless</a> </p> <a href="https://publications.waset.org/abstracts/182407/finite-sum-optimization-adaptivity-to-smoothness-and-loopless-variance-reduction" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/182407.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">70</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3310</span> Optimization of Structures with Mixed Integer Non-linear Programming (MINLP)</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Stojan%20Kravanja">Stojan Kravanja</a>, <a href="https://publications.waset.org/abstracts/search?q=Andrej%20Ivani%C4%8D"> Andrej Ivanič</a>, <a href="https://publications.waset.org/abstracts/search?q=Toma%C5%BE%20%C5%BDula"> Tomaž Žula</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This contribution focuses on structural optimization in civil engineering using mixed integer non-linear programming (MINLP). MINLP is characterized as a versatile method that can handle both continuous and discrete optimization variables simultaneously. Continuous variables are used to optimize parameters such as dimensions, stresses, masses, or costs, while discrete variables represent binary decisions to determine the presence or absence of structural elements within a structure while also calculating discrete materials and standard sections. The optimization process is divided into three main steps. First, a mechanical superstructure with a variety of different topology-, material- and dimensional alternatives. Next, a MINLP model is formulated to encapsulate the optimization problem. Finally, an optimal solution is searched in the direction of the defined objective function while respecting the structural constraints. The economic or mass objective function of the material and labor costs of a structure is subjected to the constraints known from structural analysis. These constraints include equations for the calculation of internal forces and deflections, as well as equations for the dimensioning of structural components (in accordance with the Eurocode standards). Given the complex, non-convex and highly non-linear nature of optimization problems in civil engineering, the Modified Outer-Approximation/Equality-Relaxation (OA/ER) algorithm is applied. This algorithm alternately solves subproblems of non-linear programming (NLP) and main problems of mixed-integer linear programming (MILP), in this way gradually refines the solution space up to the optimal solution. The NLP corresponds to the continuous optimization of parameters (with fixed topology, discrete materials and standard dimensions, all determined in the previous MILP), while the MILP involves a global approximation to the superstructure of alternatives, where a new topology, materials, standard dimensions are determined. The optimization of a convex problem is stopped when the MILP solution becomes better than the best NLP solution. Otherwise, it is terminated when the NLP solution can no longer be improved. While the OA/ER algorithm, like all other algorithms, does not guarantee global optimality due to the presence of non-convex functions, various modifications, including convexity tests, are implemented in OA/ER to mitigate these difficulties. The effectiveness of the proposed MINLP approach is demonstrated by its application to various structural optimization tasks, such as mass optimization of steel buildings, cost optimization of timber halls, composite floor systems, etc. Special optimization models have been developed for the optimization of these structures. The MINLP optimizations, facilitated by the user-friendly software package MIPSYN, provide insights into a mass or cost-optimal solutions, optimal structural topologies, optimal material and standard cross-section choices, confirming MINLP as a valuable method for the optimization of structures in civil engineering. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=MINLP" title="MINLP">MINLP</a>, <a href="https://publications.waset.org/abstracts/search?q=mixed-integer%20non-linear%20programming" title=" mixed-integer non-linear programming"> mixed-integer non-linear programming</a>, <a href="https://publications.waset.org/abstracts/search?q=optimization" title=" optimization"> optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=structures" title=" structures"> structures</a> </p> <a href="https://publications.waset.org/abstracts/185274/optimization-of-structures-with-mixed-integer-non-linear-programming-minlp" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/185274.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">46</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3309</span> Load Management Using Multiple Sequential Load Shaping Techniques</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Amira%20M.%20Attia">Amira M. Attia</a>, <a href="https://publications.waset.org/abstracts/search?q=Karim%20H.%20Youssef"> Karim H. Youssef</a>, <a href="https://publications.waset.org/abstracts/search?q=Nabil%20H.%20Abbasi"> Nabil H. Abbasi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Demand Side Management (DSM) is an essential characteristic of current and future smart grid systems. As one of DSM functions, load management aims to control customers’ total electric consumption and utility’s load factor by using various load shaping techniques. However, applying load shaping techniques such as load shifting, peak clipping, or strategic conservation individually does not provide the desired level of improvement for load factor increment and/or customer’s bill reduction. In this paper, two load shaping techniques will be simulated as constrained optimization problems. The purpose is to reflect the application of combined load shifting and strategic conservation model together at the same time, and the application of combined load shifting and peak clipping model as well. The problem will be formulated and solved by using disciplined convex programming (CVX) based MATLAB® R2013b. Simulation results will be evaluated and compared for studying the most impactful multi-techniques model in improving load curve. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=convex%20programing" title="convex programing">convex programing</a>, <a href="https://publications.waset.org/abstracts/search?q=demand%20side%20management" title=" demand side management"> demand side management</a>, <a href="https://publications.waset.org/abstracts/search?q=load%20shaping" title=" load shaping"> load shaping</a>, <a href="https://publications.waset.org/abstracts/search?q=multiple" title=" multiple"> multiple</a>, <a href="https://publications.waset.org/abstracts/search?q=building%20energy%20optimization" title=" building energy optimization"> building energy optimization</a> </p> <a href="https://publications.waset.org/abstracts/91746/load-management-using-multiple-sequential-load-shaping-techniques" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/91746.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">313</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3308</span> Market Solvency Capital Requirement Minimization: How Non-linear Solvers Provide Portfolios Complying with Solvency II Regulation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Abraham%20Castellanos">Abraham Castellanos</a>, <a href="https://publications.waset.org/abstracts/search?q=Christophe%20Durville"> Christophe Durville</a>, <a href="https://publications.waset.org/abstracts/search?q=Sophie%20Echenim"> Sophie Echenim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this article, a portfolio optimization problem is performed in a Solvency II context: it illustrates how advanced optimization techniques can help to tackle complex operational pain points around the monitoring, control, and stability of Solvency Capital Requirement (SCR). The market SCR of a portfolio is calculated as a combination of SCR sub-modules. These sub-modules are the results of stress-tests on interest rate, equity, property, credit and FX factors, as well as concentration on counter-parties. The market SCR is non convex and non differentiable, which does not make it a natural optimization criteria candidate. In the SCR formulation, correlations between sub-modules are fixed, whereas risk-driven portfolio allocation is usually driven by the dynamics of the actual correlations. Implementing a portfolio construction approach that is efficient on both a regulatory and economic standpoint is not straightforward. Moreover, the challenge for insurance portfolio managers is not only to achieve a minimal SCR to reduce non-invested capital but also to ensure stability of the SCR. Some optimizations have already been performed in the literature, simplifying the standard formula into a quadratic function. But to our knowledge, it is the first time that the standard formula of the market SCR is used in an optimization problem. Two solvers are combined: a bundle algorithm for convex non- differentiable problems, and a BFGS (Broyden-Fletcher-Goldfarb- Shanno)-SQP (Sequential Quadratic Programming) algorithm, to cope with non-convex cases. A market SCR minimization is then performed with historical data. This approach results in significant reduction of the capital requirement, compared to a classical Markowitz approach based on the historical volatility. A comparative analysis of different optimization models (equi-risk-contribution portfolio, minimizing volatility portfolio and minimizing value-at-risk portfolio) is performed and the impact of these strategies on risk measures including market SCR and its sub-modules is evaluated. A lack of diversification of market SCR is observed, specially for equities. This was expected since the market SCR strongly penalizes this type of financial instrument. It was shown that this direct effect of the regulation can be attenuated by implementing constraints in the optimization process or minimizing the market SCR together with the historical volatility, proving the interest of having a portfolio construction approach that can incorporate such features. The present results are further explained by the Market SCR modelling. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=financial%20risk" title="financial risk">financial risk</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20optimization" title=" numerical optimization"> numerical optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=portfolio%20management" title=" portfolio management"> portfolio management</a>, <a href="https://publications.waset.org/abstracts/search?q=solvency%20capital%20requirement" title=" solvency capital requirement"> solvency capital requirement</a> </p> <a href="https://publications.waset.org/abstracts/127464/market-solvency-capital-requirement-minimization-how-non-linear-solvers-provide-portfolios-complying-with-solvency-ii-regulation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/127464.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">117</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3307</span> Parameterized Lyapunov Function Based Robust Diagonal Dominance Pre-Compensator Design for Linear Parameter Varying Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Xiaobao%20Han">Xiaobao Han</a>, <a href="https://publications.waset.org/abstracts/search?q=Huacong%20Li"> Huacong Li</a>, <a href="https://publications.waset.org/abstracts/search?q=Jia%20Li"> Jia Li</a> </p> <p class="card-text"><strong>Abstract:</strong></p> For dynamic decoupling of linear parameter varying system, a robust dominance pre-compensator design method is given. The parameterized pre-compensator design problem is converted into optimal problem constrained with parameterized linear matrix inequalities (PLMI); To solve this problem, firstly, this optimization problem is equivalently transformed into a new form with elimination of coupling relationship between parameterized Lyapunov function (PLF) and pre-compensator. Then the problem was reduced to a normal convex optimization problem with normal linear matrix inequalities (LMI) constraints on a newly constructed convex polyhedron. Moreover, a parameter scheduling pre-compensator was achieved, which satisfies robust performance and decoupling performances. Finally, the feasibility and validity of the robust diagonal dominance pre-compensator design method are verified by the numerical simulation of a turbofan engine PLPV model. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=linear%20parameter%20varying%20%28LPV%29" title="linear parameter varying (LPV)">linear parameter varying (LPV)</a>, <a href="https://publications.waset.org/abstracts/search?q=parameterized%20Lyapunov%20function%20%28PLF%29" title=" parameterized Lyapunov function (PLF)"> parameterized Lyapunov function (PLF)</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20matrix%20inequalities%20%28LMI%29" title=" linear matrix inequalities (LMI)"> linear matrix inequalities (LMI)</a>, <a href="https://publications.waset.org/abstracts/search?q=diagonal%20dominance%20pre-compensator" title=" diagonal dominance pre-compensator"> diagonal dominance pre-compensator</a> </p> <a href="https://publications.waset.org/abstracts/57964/parameterized-lyapunov-function-based-robust-diagonal-dominance-pre-compensator-design-for-linear-parameter-varying-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/57964.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">399</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3306</span> Convex Restrictions for Outage Constrained MU-MISO Downlink under Imperfect Channel State Information</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20Preetha%20Priyadharshini">A. Preetha Priyadharshini</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20B.%20M.%20Priya"> S. B. M. Priya</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we consider the MU-MISO downlink scenario, under imperfect channel state information (CSI). The main issue in imperfect CSI is to keep the probability of each user achievable outage rate below the given threshold level. Such a rate outage constraints present significant and analytical challenges. There are many probabilistic methods are used to minimize the transmit optimization problem under imperfect CSI. Here, decomposition based large deviation inequality and Bernstein type inequality convex restriction methods are used to perform the optimization problem under imperfect CSI. These methods are used for achieving improved output quality and lower complexity. They provide a safe tractable approximation of the original rate outage constraints. Based on these method implementations, performance has been evaluated in the terms of feasible rate and average transmission power. The simulation results are shown that all the two methods offer significantly improved outage quality and lower computational complexity. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=imperfect%20channel%20state%20information" title="imperfect channel state information">imperfect channel state information</a>, <a href="https://publications.waset.org/abstracts/search?q=outage%20probability" title=" outage probability"> outage probability</a>, <a href="https://publications.waset.org/abstracts/search?q=multiuser-%20multi%20input%20single%20output" title=" multiuser- multi input single output"> multiuser- multi input single output</a>, <a href="https://publications.waset.org/abstracts/search?q=channel%20state%20information" title=" channel state information"> channel state information</a> </p> <a href="https://publications.waset.org/abstracts/48521/convex-restrictions-for-outage-constrained-mu-miso-downlink-under-imperfect-channel-state-information" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/48521.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">813</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3305</span> Solving Nonconvex Economic Load Dispatch Problem Using Particle Swarm Optimization with Time Varying Acceleration Coefficients</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Alireza%20Alizadeh">Alireza Alizadeh</a>, <a href="https://publications.waset.org/abstracts/search?q=Hossein%20Ghadimi"> Hossein Ghadimi</a>, <a href="https://publications.waset.org/abstracts/search?q=Oveis%20Abedinia"> Oveis Abedinia</a>, <a href="https://publications.waset.org/abstracts/search?q=Noradin%20Ghadimi"> Noradin Ghadimi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A Particle Swarm Optimization with Time Varying Acceleration Coefficients (PSO-TVAC) is proposed to determine optimal economic load dispatch (ELD) problem in this paper. The proposed methodology easily takes care of solving non-convex economic load dispatch problems along with different constraints like transmission losses, dynamic operation constraints and prohibited operating zones. The proposed approach has been implemented on the 3-machines 6-bus, IEEE 5-machines 14-bus, IEEE 6-machines 30-bus systems and 13 thermal units power system. The proposed technique is compared to solve the ELD problem with hybrid approach by using the valve-point effect. The comparison results prove the capability of the proposed method giving significant improvements in the generation cost for the economic load dispatch problem. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=PSO-TVAC" title="PSO-TVAC">PSO-TVAC</a>, <a href="https://publications.waset.org/abstracts/search?q=economic%20load%20dispatch" title=" economic load dispatch"> economic load dispatch</a>, <a href="https://publications.waset.org/abstracts/search?q=non-convex%20cost%20function" title=" non-convex cost function"> non-convex cost function</a>, <a href="https://publications.waset.org/abstracts/search?q=prohibited%20operating%20zone" title=" prohibited operating zone"> prohibited operating zone</a>, <a href="https://publications.waset.org/abstracts/search?q=transmission%20losses" title=" transmission losses"> transmission losses</a> </p> <a href="https://publications.waset.org/abstracts/13428/solving-nonconvex-economic-load-dispatch-problem-using-particle-swarm-optimization-with-time-varying-acceleration-coefficients" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/13428.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">387</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3304</span> Solving Linear Systems Involved in Convex Programming Problems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yixun%20Shi">Yixun Shi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Many interior point methods for convex programming solve an (n+m)x(n+m)linear system in each iteration. Many implementations solve this system in each iteration by considering an equivalent mXm system (4) as listed in the paper, and thus the job is reduced into solving the system (4). However, the system(4) has to be solved exactly since otherwise the error would be entirely passed onto the last m equations of the original system. Often the Cholesky factorization is computed to obtain the exact solution of (4). One Cholesky factorization is to be done in every iteration, resulting in higher computational costs. In this paper, two iterative methods for solving linear systems using vector division are combined together and embedded into interior point methods. Instead of computing one Cholesky factorization in each iteration, it requires only one Cholesky factorization in the entire procedure, thus significantly reduces the amount of computation needed for solving the problem. Based on that, a hybrid algorithm for solving convex programming problems is proposed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=convex%20programming" title="convex programming">convex programming</a>, <a href="https://publications.waset.org/abstracts/search?q=interior%20point%20method" title=" interior point method"> interior point method</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20systems" title=" linear systems"> linear systems</a>, <a href="https://publications.waset.org/abstracts/search?q=vector%20division" title=" vector division"> vector division</a> </p> <a href="https://publications.waset.org/abstracts/39573/solving-linear-systems-involved-in-convex-programming-problems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/39573.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">402</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3303</span> Network Analysis and Sex Prediction based on a full Human Brain Connectome</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Oleg%20Vlasovets">Oleg Vlasovets</a>, <a href="https://publications.waset.org/abstracts/search?q=Fabian%20Schaipp"> Fabian Schaipp</a>, <a href="https://publications.waset.org/abstracts/search?q=Christian%20L.%20Mueller"> Christian L. Mueller</a> </p> <p class="card-text"><strong>Abstract:</strong></p> we conduct a network analysis and predict the sex of 1000 participants based on ”connectome” - pairwise Pearson’s correlation across 436 brain parcels. We solve the non-smooth convex optimization problem, known under the name of Graphical Lasso, where the solution includes a low-rank component. With this solution and machine learning model for a sex prediction, we explain the brain parcels-sex connectivity patterns. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=network%20analysis" title="network analysis">network analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=neuroscience" title=" neuroscience"> neuroscience</a>, <a href="https://publications.waset.org/abstracts/search?q=machine%20learning" title=" machine learning"> machine learning</a>, <a href="https://publications.waset.org/abstracts/search?q=optimization" title=" optimization"> optimization</a> </p> <a href="https://publications.waset.org/abstracts/146685/network-analysis-and-sex-prediction-based-on-a-full-human-brain-connectome" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/146685.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">147</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3302</span> Development of Algorithms for Solving and Analyzing Special Problems Transports Type</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Dmitri%20Terzi">Dmitri Terzi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The article presents the results of an algorithmic study of a special optimization problem of the transport type (traveling salesman problem): 1) To solve the problem, a new natural algorithm has been developed based on the decomposition of the initial data into convex hulls, which has a number of advantages; it is applicable for a fairly large dimension, does not require a large amount of memory, and has fairly good performance. The relevance of the algorithm lies in the fact that, in practice, programs for problems with the number of traversal points of no more than twenty are widely used. For large-scale problems, the availability of algorithms and programs of this kind is difficult. The proposed algorithm is natural because the optimal solution found by the exact algorithm is not always feasible due to the presence of many other factors that may require some additional restrictions. 2) Another inverse problem solved here is to describe a class of traveling salesman problems that have a predetermined optimal solution. The constructed algorithm 2 allows us to characterize the structure of traveling salesman problems, as well as construct test problems to evaluate the effectiveness of algorithms and other purposes. 3) The appendix presents a software implementation of Algorithm 1 (in MATLAB), which can be used to solve practical problems, as well as in the educational process on operations research and optimization methods. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=traveling%20salesman%20problem" title="traveling salesman problem">traveling salesman problem</a>, <a href="https://publications.waset.org/abstracts/search?q=solution%20construction%20algorithm" title=" solution construction algorithm"> solution construction algorithm</a>, <a href="https://publications.waset.org/abstracts/search?q=convex%20hulls" title=" convex hulls"> convex hulls</a>, <a href="https://publications.waset.org/abstracts/search?q=optimality%20verification" title=" optimality verification"> optimality verification</a> </p> <a href="https://publications.waset.org/abstracts/179041/development-of-algorithms-for-solving-and-analyzing-special-problems-transports-type" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/179041.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">73</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3301</span> Improved Artificial Bee Colony Algorithm for Non-Convex Economic Power Dispatch Problem </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Badr%20M.%20Alshammari">Badr M. Alshammari</a>, <a href="https://publications.waset.org/abstracts/search?q=T.%20Guesmi"> T. Guesmi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This study presents a modified version of the artificial bee colony (ABC) algorithm by including a local search technique for solving the non-convex economic power dispatch problem. The local search step is incorporated at the end of each iteration. Total system losses, valve-point loading effects and prohibited operating zones have been incorporated in the problem formulation. Thus, the problem becomes highly nonlinear and with discontinuous objective function. The proposed technique is validated using an IEEE benchmark system with ten thermal units. Simulation results demonstrate that the proposed optimization algorithm has better convergence characteristics in comparison with the original ABC algorithm. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=economic%20power%20dispatch" title="economic power dispatch">economic power dispatch</a>, <a href="https://publications.waset.org/abstracts/search?q=artificial%20bee%20colony" title=" artificial bee colony"> artificial bee colony</a>, <a href="https://publications.waset.org/abstracts/search?q=valve-point%20loading%20effects" title=" valve-point loading effects"> valve-point loading effects</a>, <a href="https://publications.waset.org/abstracts/search?q=prohibited%20operating%20zones" title=" prohibited operating zones"> prohibited operating zones</a> </p> <a href="https://publications.waset.org/abstracts/89937/improved-artificial-bee-colony-algorithm-for-non-convex-economic-power-dispatch-problem" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/89937.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">257</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3300</span> Some Integral Inequalities of Hermite-Hadamard Type on Time Scale and Their Applications</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Artion%20Kashuri">Artion Kashuri</a>, <a href="https://publications.waset.org/abstracts/search?q=Rozana%20Liko"> Rozana Liko</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the authors establish an integral identity using delta differentiable functions. By applying this identity, some new results via a general class of convex functions with respect to two nonnegative functions on a time scale are given. Also, for suitable choices of nonnegative functions, some special cases are deduced. Finally, in order to illustrate the efficiency of our main results, some applications to special means are obtained as well. We hope that current work using our idea and technique will attract the attention of researchers working in mathematical analysis, mathematical inequalities, numerical analysis, special functions, fractional calculus, quantum mechanics, quantum calculus, physics, probability and statistics, differential and difference equations, optimization theory, and other related fields in pure and applied sciences. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=convex%20functions" title="convex functions">convex functions</a>, <a href="https://publications.waset.org/abstracts/search?q=Hermite-Hadamard%20inequality" title=" Hermite-Hadamard inequality"> Hermite-Hadamard inequality</a>, <a href="https://publications.waset.org/abstracts/search?q=special%20means" title=" special means"> special means</a>, <a href="https://publications.waset.org/abstracts/search?q=time%20scale" title=" time scale"> time scale</a> </p> <a href="https://publications.waset.org/abstracts/133550/some-integral-inequalities-of-hermite-hadamard-type-on-time-scale-and-their-applications" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/133550.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">150</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3299</span> Optimal Dynamic Economic Load Dispatch Using Artificial Immune System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=I.%20A.%20Farhat">I. A. Farhat</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The dynamic economic dispatch (DED) problem is one of the complex, constrained optimization problems that have nonlinear, con-convex and non-smooth objective functions. The purpose of the DED is to determine the optimal economic operation of the committed units while meeting the load demand. Associated to this constrained problem there exist highly nonlinear and non-convex practical constraints to be satisfied. Therefore, classical and derivative-based methods are likely not to converge to an optimal or near optimal solution to such a dynamic and large-scale problem. In this paper, an Artificial Immune System technique (AIS) is implemented and applied to solve the DED problem considering the transmission power losses and the valve-point effects in addition to the other operational constraints. To demonstrate the effectiveness of the proposed technique, two case studies are considered. The results obtained using the AIS are compared to those obtained by other methods reported in the literature and found better. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=artificial%20immune%20system" title="artificial immune system">artificial immune system</a>, <a href="https://publications.waset.org/abstracts/search?q=dynamic%20economic%20dispatch" title=" dynamic economic dispatch"> dynamic economic dispatch</a>, <a href="https://publications.waset.org/abstracts/search?q=optimal%20economic%20operation" title=" optimal economic operation"> optimal economic operation</a>, <a href="https://publications.waset.org/abstracts/search?q=large-scale%20problem" title=" large-scale problem"> large-scale problem</a> </p> <a href="https://publications.waset.org/abstracts/4838/optimal-dynamic-economic-load-dispatch-using-artificial-immune-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/4838.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">236</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3298</span> The Possibility of Solving a 3x3 Rubik’s Cube under 3 Seconds</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chung%20To%20Kong">Chung To Kong</a>, <a href="https://publications.waset.org/abstracts/search?q=Siu%20Ming%20Yiu"> Siu Ming Yiu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Rubik's cube was invented in 1974. Since then, speedcubers all over the world try their best to break the world record again and again. The newest record is 3.47 seconds. There are many factors that affect the timing, including turns per second (tps), algorithm, finger trick, hardware of the cube. In this paper, the lower bound of the cube solving time will be discussed using convex optimization. Extended analysis of the world records will be used to understand how to improve the timing. With the understanding of each part of the solving step, the paper suggests a list of speed improvement techniques. Based on the analysis of the world record, there is a high possibility that the 3 seconds mark will be broken soon. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Rubik%27s%20Cube" title="Rubik's Cube">Rubik's Cube</a>, <a href="https://publications.waset.org/abstracts/search?q=speed" title=" speed"> speed</a>, <a href="https://publications.waset.org/abstracts/search?q=finger%20trick" title=" finger trick"> finger trick</a>, <a href="https://publications.waset.org/abstracts/search?q=optimization" title=" optimization"> optimization</a> </p> <a href="https://publications.waset.org/abstracts/138171/the-possibility-of-solving-a-3x3-rubiks-cube-under-3-seconds" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/138171.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">206</span> </span> </div> </div> <ul class="pagination"> <li class="page-item disabled"><span class="page-link">&lsaquo;</span></li> <li class="page-item active"><span class="page-link">1</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=convex%20optimization&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=convex%20optimization&page=3">3</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=convex%20optimization&page=4">4</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=convex%20optimization&page=5">5</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=convex%20optimization&page=6">6</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=convex%20optimization&page=7">7</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=convex%20optimization&page=8">8</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=convex%20optimization&page=9">9</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=convex%20optimization&page=10">10</a></li> <li class="page-item disabled"><span class="page-link">...</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=convex%20optimization&page=110">110</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=convex%20optimization&page=111">111</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=convex%20optimization&page=2" rel="next">&rsaquo;</a></li> </ul> </div> </main> <footer> <div id="infolinks" class="pt-3 pb-2"> <div class="container"> <div style="background-color:#f5f5f5;" class="p-3"> <div class="row"> <div class="col-md-2"> <ul class="list-unstyled"> About <li><a href="https://waset.org/page/support">About Us</a></li> <li><a href="https://waset.org/page/support#legal-information">Legal</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/WASET-16th-foundational-anniversary.pdf">WASET celebrates its 16th foundational anniversary</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Account <li><a href="https://waset.org/profile">My Account</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Explore <li><a href="https://waset.org/disciplines">Disciplines</a></li> <li><a href="https://waset.org/conferences">Conferences</a></li> <li><a href="https://waset.org/conference-programs">Conference Program</a></li> <li><a href="https://waset.org/committees">Committees</a></li> <li><a href="https://publications.waset.org">Publications</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Research <li><a href="https://publications.waset.org/abstracts">Abstracts</a></li> <li><a href="https://publications.waset.org">Periodicals</a></li> <li><a href="https://publications.waset.org/archive">Archive</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Open Science <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Science-Philosophy.pdf">Open Science Philosophy</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Science-Award.pdf">Open Science Award</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Society-Open-Science-and-Open-Innovation.pdf">Open Innovation</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Postdoctoral-Fellowship-Award.pdf">Postdoctoral Fellowship Award</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Scholarly-Research-Review.pdf">Scholarly Research Review</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Support <li><a href="https://waset.org/page/support">Support</a></li> <li><a href="https://waset.org/profile/messages/create">Contact Us</a></li> <li><a href="https://waset.org/profile/messages/create">Report Abuse</a></li> </ul> </div> </div> </div> </div> </div> <div class="container text-center"> <hr style="margin-top:0;margin-bottom:.3rem;"> <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank" class="text-muted small">Creative Commons Attribution 4.0 International License</a> <div id="copy" class="mt-2">© 2024 World Academy of Science, Engineering and Technology</div> </div> </footer> <a href="javascript:" id="return-to-top"><i class="fas fa-arrow-up"></i></a> <div class="modal" id="modal-template"> <div class="modal-dialog"> <div class="modal-content"> <div class="row m-0 mt-1"> <div class="col-md-12"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> </div> </div> <div class="modal-body"></div> </div> </div> </div> <script src="https://cdn.waset.org/static/plugins/jquery-3.3.1.min.js"></script> <script src="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/js/bootstrap.bundle.min.js"></script> <script src="https://cdn.waset.org/static/js/site.js?v=150220211556"></script> <script> jQuery(document).ready(function() { /*jQuery.get("https://publications.waset.org/xhr/user-menu", function (response) { jQuery('#mainNavMenu').append(response); });*/ jQuery.get({ url: "https://publications.waset.org/xhr/user-menu", cache: false }).then(function(response){ jQuery('#mainNavMenu').append(response); }); }); </script> </body> </html>