Two error bounds for constrained optimization problems and their applications
type: Item
instance of: scholarly article
title: Two error bounds for constrained optimization problems and their applications
zbMATH Open document ID: 1173.65045
author: Changyu Wang
author: Wenling Zhao
author: Jianzhong Zhang
published in: Applied Mathematics and Optimization
publication date: 2009-06-08T00:00:00Z
review text: The trust region method is a popular method for solving constrained optimization problem and there is a lot of literature about it. The aim of this paper is to study a global error bound for the projected gradient and a local error bound for the distance from a feasible solution to the optimal solution set of a nonlinear programming problem by using some characteristic quantities such as value function, trust region radius etc., which appeared in the trust region method. As applications of these error bounds, the authors obtain sufficient conditions under which a sequence of feasible solutions converges to a stationary point or to an optimal solution , respectively, and a necessary and sufficient condition under which a sequence of feasible solutions converges to a Kuhn-Tucker point. Other applications involve finite termination of a sequence of feasible solutions. For general optimization problems, when the optimal solution set is generalized non-degenerate or gives generalized weak sharp minima, the authors give a necessary and sufficient condition for a sequence of feasible solutions to terminate finitely at a Kuhn-Tucker point, and a sufficient condition which guarantees that a sequence of feasible solutions terminates finitely at a stationary point.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C34
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 90C51
zbMATH DE Number: 5562554
zbMATH Keywords: Trust region subproblem
zbMATH Keywords: value function
zbMATH Keywords: projected gradient
zbMATH Keywords: error bound
zbMATH Keywords: finite termination
zbMATH Keywords: constrained optimization
zbMATH Keywords: nonlinear programming
zbMATH Keywords: trust region method
zbMATH Keywords: Kuhn-Tucker point
reviewed by: Nada Djuranović-Miličić
MaRDI profile type: Publication
full work available at URL: s00245-007-9023-8
OpenAlex ID: W2047074228
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DOI: 10.1007/S00245-007-9023-8
description: scientific article; zbMATH DE number 5562554