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analysis</title> <meta name="description" content="Search results for: convex analysis"> <meta name="keywords" content="convex analysis"> <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 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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 analysis"> <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> 27926</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: convex analysis</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">27926</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">27925</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">27924</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">27923</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">27922</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">27921</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">27920</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">27919</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">27918</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">27917</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">27916</span> Measuring Development through Extreme Observations: An Archetypal Analysis Approach to Index Construction</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Claudeline%20D.%20Cellan">Claudeline D. Cellan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Development is multifaceted, and efforts to hasten growth in all these facets have been gaining traction in recent years. Thus, producing a composite index that is reflective of these multidimensional impacts captures the interests of policymakers. The problem lies in going through a mixture of theoretical, methodological and empirical decisions and complexities which, when done carelessly, can lead to inconsistent and unreliable results. This study looks into index computation from a different and less complex perspective. Borrowing the idea of archetypes or ‘pure types’, archetypal analysis looks for points in the convex hull of the multivariate data set that captures as much information in the data as possible. The archetypes or 'pure types' are estimated such that they are convex combinations of all the observations, which in turn are convex combinations of the archetypes. This ensures that the archetypes are realistically observable, therefore achievable. In the sense of composite indices, we look for the best among these archetypes and use this as a benchmark for index computation. Its straightforward and simplistic approach does away with aggregation and substitutability problems which are commonly encountered in index computation. As an example of the application of archetypal analysis in index construction, the country data for the Human Development Index (HDI 2017) of the United Nations Development Programme (UNDP) is used. The goal of this exercise is not to replicate the result of the UNDP-computed HDI, but to illustrate the usability of archetypal analysis in index construction. Here best is defined in the context of life, education and gross national income sub-indices. Results show that the HDI from the archetypal analysis has a linear relationship with the UNDP-computed HDI. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=archetypes" title="archetypes">archetypes</a>, <a href="https://publications.waset.org/abstracts/search?q=composite%20index" title=" composite index"> composite index</a>, <a href="https://publications.waset.org/abstracts/search?q=convex%20combination" title=" convex combination"> convex combination</a>, <a href="https://publications.waset.org/abstracts/search?q=development" title=" development"> development</a> </p> <a href="https://publications.waset.org/abstracts/107237/measuring-development-through-extreme-observations-an-archetypal-analysis-approach-to-index-construction" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/107237.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">128</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">27915</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">27914</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">27913</span> Comparison of the Boundary Element Method and the Method of Fundamental Solutions for Analysis of Potential and Elasticity</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=S.%20Zenhari">S. Zenhari</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20R.%20Hematiyan"> M. R. Hematiyan</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Khosravifard"> A. Khosravifard</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20R.%20Feizi"> M. R. Feizi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The boundary element method (BEM) and the method of fundamental solutions (MFS) are well-known fundamental solution-based methods for solving a variety of problems. Both methods are boundary-type techniques and can provide accurate results. In comparison to the finite element method (FEM), which is a domain-type method, the BEM and the MFS need less manual effort to solve a problem. The aim of this study is to compare the accuracy and reliability of the BEM and the MFS. This comparison is made for 2D potential and elasticity problems with different boundary and loading conditions. In the comparisons, both convex and concave domains are considered. Both linear and quadratic elements are employed for boundary element analysis of the examples. The discretization of the problem domain in the BEM, i.e., converting the boundary of the problem into boundary elements, is relatively simple; however, in the MFS, obtaining appropriate locations of collocation and source points needs more attention to obtain reliable solutions. The results obtained from the presented examples show that both methods lead to accurate solutions for convex domains, whereas the BEM is more suitable than the MFS for concave domains. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=boundary%20element%20method" title="boundary element method">boundary element method</a>, <a href="https://publications.waset.org/abstracts/search?q=method%20of%20fundamental%20solutions" title=" method of fundamental solutions"> method of fundamental solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=elasticity" title=" elasticity"> elasticity</a>, <a href="https://publications.waset.org/abstracts/search?q=potential%20problem" title=" potential problem"> potential problem</a>, <a href="https://publications.waset.org/abstracts/search?q=convex%20domain" title=" convex domain"> convex domain</a>, <a href="https://publications.waset.org/abstracts/search?q=concave%20domain" title=" concave domain"> concave domain</a> </p> <a href="https://publications.waset.org/abstracts/163380/comparison-of-the-boundary-element-method-and-the-method-of-fundamental-solutions-for-analysis-of-potential-and-elasticity" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/163380.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">90</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">27912</span> Optimum Design of Hybrid (Metal-Composite) Mechanical Power Transmission System under Uncertainty by Convex Modelling</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sfiso%20Radebe">Sfiso Radebe</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The design models dealing with flawless composite structures are in abundance, where the mechanical properties of composite structures are assumed to be known a priori. However, if the worst case scenario is assumed, where material defects combined with processing anomalies in composite structures are expected, a different solution is attained. Furthermore, if the system being designed combines in series hybrid elements, individually affected by material constant variations, it implies that a different approach needs to be taken. In the body of literature, there is a compendium of research that investigates different modes of failure affecting hybrid metal-composite structures. It covers areas pertaining to the failure of the hybrid joints, structural deformation, transverse displacement, the suppression of vibration and noise. In the present study a system employing a combination of two or more hybrid power transmitting elements will be explored for the least favourable dynamic loads as well as weight minimization, subject to uncertain material properties. Elastic constants are assumed to be uncertain-but-bounded quantities varying slightly around their nominal values where the solution is determined using convex models of uncertainty. Convex analysis of the problem leads to the computation of the least favourable solution and ultimately to a robust design. This approach contrasts with a deterministic analysis where the average values of elastic constants are employed in the calculations, neglecting the variations in the material properties. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=convex%20modelling" title="convex modelling">convex modelling</a>, <a href="https://publications.waset.org/abstracts/search?q=hybrid" title=" hybrid"> hybrid</a>, <a href="https://publications.waset.org/abstracts/search?q=metal-composite" title=" metal-composite"> metal-composite</a>, <a href="https://publications.waset.org/abstracts/search?q=robust%20design" title=" robust design"> robust design</a> </p> <a href="https://publications.waset.org/abstracts/76900/optimum-design-of-hybrid-metal-composite-mechanical-power-transmission-system-under-uncertainty-by-convex-modelling" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/76900.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">27911</span> Polarization Dependent Flexible GaN Film Nanogenerators and Electroluminescence Properties</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jeong%20Min%20Baik">Jeong Min Baik</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We present that the electroluminescence (EL) properties and electrical output power of flexible N-face p-type GaN thin films can be tuned by strain-induced piezo-potential generated across the metal-semiconductor-metal structures. Under different staining conditions (convex and concave bending modes), the transport properties of the GaN films can be changed due to the spontaneous polarization of the films. The I-V characteristics with the bending modes show that the convex bending can increase the current across the films by the decrease in the barrier height at the metal-semiconductor contact, increasing the EL intensity of the P-N junction. At convex bending, it is also shown that the flexible p-type GaN films can generate an output voltage of up to 1.0 V, while at concave bending, 0.4 V. The change of the band bending with the crystal polarity of GaN films was investigated using high-resolution photoemission spectroscopy. This study has great significance on the practical applications of GaN in optoelectronic devices and nanogenerators under a working environment. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=GaN" title="GaN">GaN</a>, <a href="https://publications.waset.org/abstracts/search?q=flexible" title=" flexible"> flexible</a>, <a href="https://publications.waset.org/abstracts/search?q=laser%20lift-off" title=" laser lift-off"> laser lift-off</a>, <a href="https://publications.waset.org/abstracts/search?q=nanogenerator" title=" nanogenerator"> nanogenerator</a> </p> <a href="https://publications.waset.org/abstracts/13583/polarization-dependent-flexible-gan-film-nanogenerators-and-electroluminescence-properties" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/13583.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">419</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">27910</span> The Algorithm to Solve the Extend General Malfatti’s Problem in a Convex Circular Triangle</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ching-Shoei%20Chiang">Ching-Shoei Chiang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The Malfatti’s Problem solves the problem of fitting 3 circles into a right triangle such that these 3 circles are tangent to each other, and each circle is also tangent to a pair of the triangle’s sides. This problem has been extended to any triangle (called general Malfatti’s Problem). Furthermore, the problem has been extended to have 1+2+…+n circles inside the triangle with special tangency properties among circles and triangle sides; we call it extended general Malfatti’s problem. In the extended general Malfatti’s problem, call it Tri(Tn), where Tn is the triangle number, there are closed-form solutions for Tri(T₁) (inscribed circle) problem and Tri(T₂) (3 Malfatti’s circles) problem. These problems become more complex when n is greater than 2. In solving Tri(Tn) problem, n>2, algorithms have been proposed to solve these problems numerically. With a similar idea, this paper proposed an algorithm to find the radii of circles with the same tangency properties. Instead of the boundary of the triangle being a straight line, we use a convex circular arc as the boundary and try to find Tn circles inside this convex circular triangle with the same tangency properties among circles and boundary Carc. We call these problems the Carc(Tn) problems. The CPU time it takes for Carc(T16) problem, which finds 136 circles inside a convex circular triangle with specified tangency properties, is less than one second. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=circle%20packing" title="circle packing">circle packing</a>, <a href="https://publications.waset.org/abstracts/search?q=computer-aided%20geometric%20design" title=" computer-aided geometric design"> computer-aided geometric design</a>, <a href="https://publications.waset.org/abstracts/search?q=geometric%20constraint%20solver" title=" geometric constraint solver"> geometric constraint solver</a>, <a href="https://publications.waset.org/abstracts/search?q=Malfatti%E2%80%99s%20problem" title=" Malfatti’s problem"> Malfatti’s problem</a> </p> <a href="https://publications.waset.org/abstracts/165851/the-algorithm-to-solve-the-extend-general-malfattis-problem-in-a-convex-circular-triangle" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/165851.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">110</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">27909</span> Investigation of the Stability of the F* Iterative Algorithm on Strong Peudocontractive Mappings and Its Applications</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Felix%20Damilola%20Ajibade">Felix Damilola Ajibade</a>, <a href="https://publications.waset.org/abstracts/search?q=Opeyemi%20O.%20Enoch"> Opeyemi O. Enoch</a>, <a href="https://publications.waset.org/abstracts/search?q=Taiwo%20Paul%20Fajusigbe"> Taiwo Paul Fajusigbe</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper is centered on conducting an inquiry into the stability of the F* iterative algorithm to the fixed point of a strongly pseudo-contractive mapping in the framework of uniformly convex Banach spaces. To achieve the desired result, certain existing inequalities in convex Banach spaces were utilized, as well as the stability criteria of Harder and Hicks. Other necessary conditions for the stability of the F* algorithm on strong pseudo-contractive mapping were also obtained. Through a numerical approach, we prove that the F* iterative algorithm is H-stable for strongly pseudo-contractive mapping. Finally, the solution of the mixed-type Volterra-Fredholm functional non-linear integral equation is estimated using our results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=stability" title="stability">stability</a>, <a href="https://publications.waset.org/abstracts/search?q=F%2A%20-iterative%20algorithm" title=" F* -iterative algorithm"> F* -iterative algorithm</a>, <a href="https://publications.waset.org/abstracts/search?q=pseudo-contractive%20mappings" title=" pseudo-contractive mappings"> pseudo-contractive mappings</a>, <a href="https://publications.waset.org/abstracts/search?q=uniformly%20convex%20Banach%20space" title=" uniformly convex Banach space"> uniformly convex Banach space</a>, <a href="https://publications.waset.org/abstracts/search?q=mixed-type%20Volterra-Fredholm%20integral%20equation" title=" mixed-type Volterra-Fredholm integral equation"> mixed-type Volterra-Fredholm integral equation</a> </p> <a href="https://publications.waset.org/abstracts/167503/investigation-of-the-stability-of-the-f-iterative-algorithm-on-strong-peudocontractive-mappings-and-its-applications" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/167503.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">103</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">27908</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">27907</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">27906</span> On the Solidness of the Polar of Recession Cones</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sima%20Hassankhali">Sima Hassankhali</a>, <a href="https://publications.waset.org/abstracts/search?q=Ildar%20Sadeqi"> Ildar Sadeqi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the theory of Pareto efficient points, the existence of a bounded base for a cone K of a normed space X is so important. In this article, we study the geometric structure of a nonzero closed convex cone K with a bounded base. For this aim, we study the structure of the polar cone K# of K. Furthermore, we obtain a necessary and sufficient condition for a nonempty closed convex set C so that its recession cone C∞ has a bounded base. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=solid%20cones" title="solid cones">solid cones</a>, <a href="https://publications.waset.org/abstracts/search?q=recession%20cones" title=" recession cones"> recession cones</a>, <a href="https://publications.waset.org/abstracts/search?q=polar%20cones" title=" polar cones"> polar cones</a>, <a href="https://publications.waset.org/abstracts/search?q=bounded%20base" title=" bounded base"> bounded base</a> </p> <a href="https://publications.waset.org/abstracts/57802/on-the-solidness-of-the-polar-of-recession-cones" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/57802.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">267</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">27905</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">27904</span> Impact of Curvatures in the Dike Line on Wave Run-up and Wave Overtopping, ConDike-Project</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Malte%20Schilling">Malte Schilling</a>, <a href="https://publications.waset.org/abstracts/search?q=Mahmoud%20M.%20Rabah"> Mahmoud M. Rabah</a>, <a href="https://publications.waset.org/abstracts/search?q=Sven%20Liebisch"> Sven Liebisch</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Wave run-up and overtopping are the relevant parameters for the dimensioning of the crest height of dikes. Various experimental as well as numerical studies have investigated these parameters under different boundary conditions (e.g. wave conditions, structure type). Particularly for the dike design in Europe, a common approach is formulated where wave and structure properties are parameterized. However, this approach assumes equal run-up heights and overtopping discharges along the longitudinal axis. However, convex dikes have a heterogeneous crest by definition. Hence, local differences in a convex dike line are expected to cause wave-structure interactions different to a straight dike. This study aims to assess both run-up and overtopping at convexly curved dikes. To cast light on the relevance of curved dikes for the design approach mentioned above, physical model tests were conducted in a 3D wave basin of the Ludwig-Franzius-Institute Hannover. A dike of a slope of 1:6 (height over length) was tested under both regular waves and TMA wave spectra. Significant wave heights ranged from 7 to 10 cm and peak periods from 1.06 to 1.79 s. Both run-up and overtopping was assessed behind the curved and straight sections of the dike. Both measurements were compared to a dike with a straight line. It was observed that convex curvatures in the longitudinal dike line cause a redirection of incident waves leading to a concentration around the center point. Measurements prove that both run-up heights and overtopping rates are higher than on the straight dike. It can be concluded that deviations from a straight longitudinal dike line have an impact on design parameters and imply uncertainties within the design approach in force. Therefore, it is recommended to consider these influencing factors for such cases. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=convex%20dike" title="convex dike">convex dike</a>, <a href="https://publications.waset.org/abstracts/search?q=longitudinal%20curvature" title=" longitudinal curvature"> longitudinal curvature</a>, <a href="https://publications.waset.org/abstracts/search?q=overtopping" title=" overtopping"> overtopping</a>, <a href="https://publications.waset.org/abstracts/search?q=run-up" title=" run-up"> run-up</a> </p> <a href="https://publications.waset.org/abstracts/71860/impact-of-curvatures-in-the-dike-line-on-wave-run-up-and-wave-overtopping-condike-project" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/71860.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">293</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">27903</span> Optimal Economic Restructuring Aimed at an Optimal Increase in GDP Constrained by a Decrease in Energy Consumption and CO2 Emissions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Alexander%20Vaninsky">Alexander Vaninsky</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The objective of this paper is finding the way of economic restructuring - that is, change in the shares of sectoral gross outputs - resulting in the maximum possible increase in the gross domestic product (GDP) combined with decreases in energy consumption and CO2 emissions. It uses an input-output model for the GDP and factorial models for the energy consumption and CO2 emissions to determine the projection of the gradient of GDP, and the antigradients of the energy consumption and CO2 emissions, respectively, on a subspace formed by the structure-related variables. Since the gradient (antigradient) provides a direction of the steepest increase (decrease) of the objective function, and their projections retain this property for the functions' limitation to the subspace, each of the three directional vectors solves a particular problem of optimal structural change. In the next step, a type of factor analysis is applied to find a convex combination of the projected gradient and antigradients having maximal possible positive correlation with each of the three. This convex combination provides the desired direction of the structural change. The national economy of the United States is used as an example of applications. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=economic%20restructuring" title="economic restructuring">economic restructuring</a>, <a href="https://publications.waset.org/abstracts/search?q=input-output%20analysis" title=" input-output analysis"> input-output analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=divisia%20index" title=" divisia index"> divisia index</a>, <a href="https://publications.waset.org/abstracts/search?q=factorial%20decomposition" title=" factorial decomposition"> factorial decomposition</a>, <a href="https://publications.waset.org/abstracts/search?q=E3%20models" title=" E3 models"> E3 models</a> </p> <a href="https://publications.waset.org/abstracts/11422/optimal-economic-restructuring-aimed-at-an-optimal-increase-in-gdp-constrained-by-a-decrease-in-energy-consumption-and-co2-emissions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/11422.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">314</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">27902</span> Analysis of Soft and Hard X-Ray Intensities Using Different Shapes of Anodes in a 4kJ Mather Type Plasma Focus Facility</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mahsa%20Mahtab">Mahsa Mahtab</a>, <a href="https://publications.waset.org/abstracts/search?q=Morteza%20Habibi"> Morteza Habibi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The effect of different anode tip geometries on the intensity of soft and hard x-ray emitted from a 4 kJ plasma focus device is investigated. For this purpose, 5 different anode tips are used. The shapes of the uppermost region of these anodes have been cylindrical-flat, cylindrical-hollow, spherical-convex, cone-flat and cone-hollow. Analyzed data have shown that cone-flat, spherical-convex and cone-hollow anodes significantly increase X-ray intensity respectively in comparison with cylindrical-flat anode; while the cylindrical-hollow tip decreases. Anode radius reduction at its end in conic or spherical anodes enhance SXR by increasing plasma density through collecting a greater mass of gas and more gradual transition phase to form a more stable dense plasma pinch. Also, HXR is enhanced by increasing the energy of electrons colliding with the anode surface through raise of induced electrical field. Finally, the cone-flat anode is introduced to use in cases in which the plasma focus device is used as an X-ray source due to its highest yield of X-ray emissions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=plasma%20focus" title="plasma focus">plasma focus</a>, <a href="https://publications.waset.org/abstracts/search?q=anode%20tip" title=" anode tip"> anode tip</a>, <a href="https://publications.waset.org/abstracts/search?q=HXR" title=" HXR"> HXR</a>, <a href="https://publications.waset.org/abstracts/search?q=SXR" title=" SXR"> SXR</a>, <a href="https://publications.waset.org/abstracts/search?q=pinched%20plasma" title=" pinched plasma"> pinched plasma</a> </p> <a href="https://publications.waset.org/abstracts/30370/analysis-of-soft-and-hard-x-ray-intensities-using-different-shapes-of-anodes-in-a-4kj-mather-type-plasma-focus-facility" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/30370.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">400</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">27901</span> Path Planning for Collision Detection between two 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> This study aimed to propose, a different architecture of a Path Planning using the NECMOP. where several nonlinear objective functions must be optimized in a conflicting situation. The ability to detect and avoid collision is very important for mobile intelligent machines. However, many artificial vision systems are not yet able to quickly and cheaply extract the wealth information. 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. This article represents a comprehensive algorithm that determine through the AMAXNET network a measure (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=path%20planning" title="path planning">path planning</a>, <a href="https://publications.waset.org/abstracts/search?q=collision%20detection" title=" collision detection"> collision detection</a>, <a href="https://publications.waset.org/abstracts/search?q=convex%20polyhedron" title=" convex polyhedron"> convex polyhedron</a>, <a href="https://publications.waset.org/abstracts/search?q=neural%20network" title=" neural network"> neural network</a> </p> <a href="https://publications.waset.org/abstracts/26616/path-planning-for-collision-detection-between-two-polyhedra" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/26616.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">438</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">27900</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">27899</span> Proximal Method of Solving Split System of Minimization Problem</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Anteneh%20Getachew%20Gebrie">Anteneh Getachew Gebrie</a>, <a href="https://publications.waset.org/abstracts/search?q=Rabian%20Wangkeeree"> Rabian Wangkeeree</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The purpose of this paper is to introduce iterative algorithm solving split system of minimization problem given as a task of ﬁnding a common minimizer point of ﬁnite family of proper, lower semicontinuous convex functions and whose image under a bounded linear operator is also common minimizer point of another ﬁnite family of proper, lower semicontinuous convex functions. We obtain strong convergence of the sequence generated by our algorithm under some suitable conditions on the parameters. The iterative schemes are developed with a way of selecting the step sizes such that the information of operator norm is not necessary. Some applications and numerical experiment is given to analyse the eﬃciency of our algorithm. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hilbert%20Space" title="Hilbert Space">Hilbert Space</a>, <a href="https://publications.waset.org/abstracts/search?q=minimization%20problems" title=" minimization problems"> minimization problems</a>, <a href="https://publications.waset.org/abstracts/search?q=Moreau-Yosida%20approximate" title=" Moreau-Yosida approximate"> Moreau-Yosida approximate</a>, <a href="https://publications.waset.org/abstracts/search?q=split%20feasibility%20problem" title=" split feasibility problem"> split feasibility problem</a> </p> <a href="https://publications.waset.org/abstracts/119147/proximal-method-of-solving-split-system-of-minimization-problem" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/119147.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">27898</span> Parental Drinking and Risky Alcohol Related Behaviors: Predicting Binge Drinking Trajectories and Their Influence on Impaired Driving among College Students</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shiran%20Bord">Shiran Bord</a>, <a href="https://publications.waset.org/abstracts/search?q=Assaf%20Oshri"> Assaf Oshri</a>, <a href="https://publications.waset.org/abstracts/search?q=Matthew%20W.%20Carlson"> Matthew W. Carlson</a>, <a href="https://publications.waset.org/abstracts/search?q=Sihong%20Liu"> Sihong Liu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Background: Alcohol-impaired driving (AID) and binge drinking are major health concerns among college students. Although the link between binge drinking and AID is well established, knowledge regarding binge drinking patterns, the factors influencing binge drinking, and the associations between consumption patterns and alcohol-related risk behaviors is lacking. Aims: To examine heterogeneous trajectories of binge drinking during college and tests factors that might predict class membership as well as class membership outcomes. Methods: Data were obtained from a sample of 1,265 college students (Mage = 18.5, SD = .66) as part of the Longitudinal Study of Violence Against Women (N = 1,265; 59.3% female; 69.2% white). Analyses were completed in three stages. First, a growth curve analysis was conducted to identify trajectories of binge drinking over time. Second, growth curve mixture modeling analyses were pursued to assess unobserved growth trajectories of binge drinking without predictors. Lastly, parental drinking variables were added to the model as predictors of class membership, and AID and being a passenger of a drunk driver were added to the model as outcomes. Results: Three binge drinking trajectories were identified: high-convex, medium concave and low-increasing. Parental drinking was associated with being in high-convex and medium-concave classes. Compared to the low-increasing class, the high convex and medium concave classes reported more AID and being a passenger of a drunk driver more frequently. Conclusions: Parental drinking may affect children’s later engagement in AID. Efforts should focus on parents' education regarding the consequences of parental modeling of alcohol consumption. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=alcohol%20impaired%20driving" title="alcohol impaired driving">alcohol impaired driving</a>, <a href="https://publications.waset.org/abstracts/search?q=alcohol%20consumption" title=" alcohol consumption"> alcohol consumption</a>, <a href="https://publications.waset.org/abstracts/search?q=binge%20drinking" title=" binge drinking"> binge drinking</a>, <a href="https://publications.waset.org/abstracts/search?q=college%20students" title=" college students"> college students</a>, <a href="https://publications.waset.org/abstracts/search?q=parental%20modeling" title=" parental modeling"> parental modeling</a> </p> <a href="https://publications.waset.org/abstracts/66974/parental-drinking-and-risky-alcohol-related-behaviors-predicting-binge-drinking-trajectories-and-their-influence-on-impaired-driving-among-college-students" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/66974.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">280</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">27897</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> <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%20analysis&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=convex%20analysis&page=3">3</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=convex%20analysis&page=4">4</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=convex%20analysis&page=5">5</a></li> <li class="page-item"><a class="page-link" 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