A stochastic algorithm for optimization problems with continua of inequalities
type: Item
instance of: scholarly article
title: A stochastic algorithm for optimization problems with continua of inequalities
zbMATH Open document ID: 0619.90069
DOI: 10.1007/BF00939413
author: B. George
published in: Journal of Optimization Theory and Applications
publication date: 1988-01-01T00:00:00Z
review text: Optimization algorithms for solving mathematical programming problems involving continua of inequalities are presented. The algorithms use an outer-approximation method, by which they attempt to approximate, at each point, the maxima of sets of inequality constraints. They do so by performing random experiments, resulting in a finite number of points, over which the maximum is taken. They use constraint-dropping schemes, by which they eliminate points from the constraint-set at hand, which are felt to be irrelevant. At each point that the algorithms construct, they evaluate a measure of optimality, which indicates the distance of the point from the set of solutions of the optimization problem. They use this measure to determine the number of random experiments performed. Thus, the number of such experiments tends to be small initially, when the points at hand are far from optimal, and they tend to increase when an optimal point is approached.
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 65K05
zbMATH DE Number: 4005997
zbMATH Keywords: outer-approximation
zbMATH Keywords: constraint-dropping
zbMATH Keywords: measure of optimality
zbMATH Keywords: stochastic algorithms
zbMATH Keywords: continua of constraints
MaRDI profile type: Publication
cites work: On Constraint Dropping Schemes and Optimality Functions for a Class of Outer Approximations Algorithms
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full work available at URL: https://doi.org/10.1007/bf00939413
OpenAlex ID: W2046263593
description: scientific article; zbMATH DE number 4005997