Gradient Projection and Conditional Gradient Methods for Constrained Nonconvex Minimization

Minimization of a smooth function on a sphere or, more generally, on a smooth manifold, is the simplest non-convex optimization problem. It has a lot of applications. Our goal is to propose a version of the gradient projection algorithm for its solution and to obtain results that guarantee convergen...

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Vydané v:	Numerical functional analysis and optimization Ročník 41; číslo 7; s. 822 - 849
Hlavní autori:	Balashov, M. V., Polyak, B. T., Tremba, A. A.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Abingdon Taylor & Francis 18.05.2020 Taylor & Francis Ltd
Predmet:	90C52. Secondary: 46N10 Algorithms Computational geometry Convergence Convexity Frank-Wolfe method gradient projection method Ležanski-Polyak-Lojasiewicz condition Manifolds Minimization on a sphere nonconvex optimization Nonlinear programming Optimization proximally smooth set smooth functions strongly convex set
ISSN:	0163-0563, 1532-2467
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Popis
Shrnutí:	Minimization of a smooth function on a sphere or, more generally, on a smooth manifold, is the simplest non-convex optimization problem. It has a lot of applications. Our goal is to propose a version of the gradient projection algorithm for its solution and to obtain results that guarantee convergence of the algorithm under some minimal natural assumptions. We use the Ležanski-Polyak-Lojasiewicz condition on a manifold to prove the global linear convergence of the algorithm. Another method well fitted for the problem is the conditional gradient (Frank-Wolfe) algorithm. We examine some conditions which guarantee global convergence of full-step version of the method with linear rate.
Bibliografia:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	0163-0563 1532-2467
DOI:	10.1080/01630563.2019.1704780