Nonmonotone algorithm for minimax optimization problems
type: Item
instance of: scholarly article
title: Nonmonotone algorithm for minimax optimization problems
zbMATH Open document ID: 1215.65114
published in: Applied Mathematics and Computation
publication date: 2011-03-28T00:00:00Z
review text: The paper deals with finite minimax optimization problems \[ \min_{x\in\mathbb{R}^n}\;\max_{1\leq i\leq m}\, f_i(x), \] where all functions \(f_i\) are twice continuously differentiable. Equivalently, the function \(\Phi(x)= \max f_i(x)\) is to minimize. The problem is not necessarily differentiable, but it is possible to transform the task to a differentiable programming problem with side conditions (inequalities). The authors introduce a nonmonotone algorithm for the construction of a minimizing sequence. The algorithm takes not only the advantage of nonmonotone strategy and second-order step but also the advantages of trust-region methods and line search methods. The new algorithm is of strongly global convergence and superlinear convergence. Numerical experiments (10 examples) indicate the efficiency.
reviewed by: Werner H. Schmidt
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 90C47
zbMATH DE Number: 5870894
zbMATH Keywords: minimax optimization problem
zbMATH Keywords: algorithm with nonmonotone strategy
zbMATH Keywords: hybrid technique
zbMATH Keywords: second-order correction
zbMATH Keywords: superlinear convergence
author: Fu-Sheng Wang
author: Yanping Wang
MaRDI profile type: Publication
full work available at URL: j.amc.2011.01.002
OpenAlex ID: W1967901732
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DOI: 10.1016/J.AMC.2011.01.002
description: scientific article; zbMATH DE number 5870894