The gradient projection algorithm for a proximally smooth set and a function with Lipschitz continuous gradient

We consider the minimization problem for a nonconvex function with Lipschitz continuous gradient on a proximally smooth (possibly nonconvex) subset of a finite-dimensional Euclidean space. We introduce the error bound condition with exponent for the gradient mapping. Under this condition, it is show...

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Bibliographic Details
Published in:Sbornik. Mathematics 2020-04, Vol.211 (4), p.481-504
Main Author: Balashov, M. V.
Format: Article
Language:English
Subjects:
Algorithms
Continuity (mathematics)
error bound condition
Euclidean geometry
Euclidean space
gradient mapping
gradient projection algorithm
Mapping
nonconvex extremal problem
Nonlinear programming
proximal smoothness
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Summary:We consider the minimization problem for a nonconvex function with Lipschitz continuous gradient on a proximally smooth (possibly nonconvex) subset of a finite-dimensional Euclidean space. We introduce the error bound condition with exponent for the gradient mapping. Under this condition, it is shown that the standard gradient projection algorithm converges to a solution of the problem linearly or sublinearly, depending on the value of the exponent . This paper is theoretical. Bibliography: 23 titles.
ISSN:1064-5616
1468-4802
DOI:10.1070/SM9214