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non-smooth</title> <meta name="description" content="Search results for: non-smooth"> <meta name="keywords" content="non-smooth"> <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 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style="font-size:.9rem"><span class="badge badge-info">3</span> Directional Implicit Functions in Nonsmooth Analysis </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Murzabekova%20Gulden">Murzabekova Gulden</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Directional implicit functions for underdetermined nonsmooth systems in terms of the new tool of the Nonsmooth analysis - exhausters are considered. A method for finding an implicit function for underdetermined nonsmooth systems is proposed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=implicit%20function" title="implicit function">implicit function</a>, <a href="https://publications.waset.org/abstracts/search?q=exhauster" title=" exhauster"> exhauster</a>, <a href="https://publications.waset.org/abstracts/search?q=nonsmooth%20systems" title=" nonsmooth systems"> nonsmooth systems</a> </p> <a href="https://publications.waset.org/abstracts/1986/directional-implicit-functions-in-nonsmooth-analysis" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/1986.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">245</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">2</span> A New Approach for Generalized First Derivative of Nonsmooth Functions Using Optimization</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohammad%20Mehdi%20Mazarei">Mohammad Mehdi Mazarei</a>, <a href="https://publications.waset.org/abstracts/search?q=Ali%20Asghar%20Behroozpoor"> Ali Asghar Behroozpoor</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we define an optimization problem corresponding to smooth and nonsmooth functions which its optimal solution is the first derivative of these functions in a domain. For this purpose, a linear programming problem corresponding to optimization problem is obtained. The optimal solution of this linear programming problem is the approximate generalized first derivative. In fact, we approximate generalized first derivative of nonsmooth functions as tailor series. We show the efficiency of our approach by some smooth and nonsmooth functions in some examples. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=general%20derivative" title="general derivative">general derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20programming" title=" linear programming"> linear programming</a>, <a href="https://publications.waset.org/abstracts/search?q=optimization%20problem" title=" optimization problem"> optimization problem</a>, <a href="https://publications.waset.org/abstracts/search?q=smooth%20and%20nonsmooth%20functions" title=" smooth and nonsmooth functions"> smooth and nonsmooth functions</a> </p> <a href="https://publications.waset.org/abstracts/19425/a-new-approach-for-generalized-first-derivative-of-nonsmooth-functions-using-optimization" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/19425.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">557</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">1</span> Second Order Optimality Conditions in Nonsmooth Analysis on Riemannian Manifolds</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Seyedehsomayeh%20Hosseini">Seyedehsomayeh Hosseini</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Much attention has been paid over centuries to understanding and solving the problem of minimization of functions. Compared to linear programming and nonlinear unconstrained optimization problems, nonlinear constrained optimization problems are much more difficult. Since the procedure of finding an optimizer is a search based on the local information of the constraints and the objective function, it is very important to develop techniques using geometric properties of the constraints and the objective function. In fact, differential geometry provides a powerful tool to characterize and analyze these geometric properties. Thus, there is clearly a link between the techniques of optimization on manifolds and standard constrained optimization approaches. Furthermore, there are manifolds that are not defined as constrained sets in R^n an important example is the Grassmann manifolds. Hence, to solve optimization problems on these spaces, intrinsic methods are used. In a nondifferentiable problem, the gradient information of the objective function generally cannot be used to determine the direction in which the function is decreasing. Therefore, techniques of nonsmooth analysis are needed to deal with such a problem. As a manifold, in general, does not have a linear structure, the usual techniques, which are often used in nonsmooth analysis on linear spaces, cannot be applied and new techniques need to be developed. This paper presents necessary and sufficient conditions for a strict local minimum of extended real-valued, nonsmooth functions defined on Riemannian manifolds. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Riemannian%20manifolds" title="Riemannian manifolds">Riemannian manifolds</a>, <a href="https://publications.waset.org/abstracts/search?q=nonsmooth%20optimization" title=" nonsmooth optimization"> nonsmooth optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=lower%20semicontinuous%20functions" title=" lower semicontinuous functions"> lower semicontinuous functions</a>, <a href="https://publications.waset.org/abstracts/search?q=subdifferential" title=" subdifferential"> subdifferential</a> </p> <a href="https://publications.waset.org/abstracts/35809/second-order-optimality-conditions-in-nonsmooth-analysis-on-riemannian-manifolds" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/35809.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">361</span> </span> </div> </div> </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); 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