A class of algorithms for large scale nonlinear minimax optimization
type: Item
instance of: scholarly article
title: A class of algorithms for large scale nonlinear minimax optimization
zbMATH Open document ID: 0595.65069
DOI: 10.1016/0096-3003(86)90004-4
published in: Applied Mathematics and Computation
publication date: 1986-01-01T00:00:00Z
review text: The author wishes to solve the nonlinear minimax problem stated as follows: (P) min F(x) subject to \(x\in X=\{x:\) \(Ax=b\), \(x\geq 0\}\), where \(F(x)=\max \{f_ i(x):\) \(i=1,2,...,m\}\) and \(f_ i\) are continuously differentiable functions defined on X. Of particular interest is the large scale case, that is, problems where the number of functions \(f_ i\) is large. Sequential linear programming and sequential quadratic programming based algorithms are often used to solve such nonlinear minimax problems. However, one of the major difficulties with such algorithms is that each iteration requires the solution of a large scale mathematical program with at least as many constraints as there are functions defining the 'max' function. The author attempts to overcome this difficulty and presents a class of sequential linear programming and sequential quadratic programming based algorithms for (P), that require, at each iteration, only a small fraction of the functions \(f_ i\). He provides proof for global convergence of this class of algorithms.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C30
zbMATH DE Number: 3958601
zbMATH Keywords: nonlinear minimax problem
zbMATH Keywords: Sequential linear programming
zbMATH Keywords: sequential quadratic programming
zbMATH Keywords: global convergence
author: Suvrajeet Sen
MaRDI profile type: Publication
full work available at URL: 0096-3003(86)90004-4
OpenAlex ID: W1975460412
cites work: An Efficient Method to Solve the Minimax Problem Directly
cites work: Q4000274
cites work: Q3928936
cites work: Q4139982
cites work: Q3912354
description: scientific article; zbMATH DE number 3958601