Penalty technique for a min-max control problem
type: Item
instance of: scholarly article
title: Penalty technique for a min-max control problem
zbMATH Open document ID: 0592.49014
DOI: 10.1007/BF00938465
published in: Journal of Optimization Theory and Applications
publication date: 1987-01-01T00:00:00Z
review text: Using relaxed controls, optimality conditions are derived for a control problem where the cost ess sup G(x,u,t) is minimized. In reformulating the problem, we impose a unilateral constraint, which we deal with by a penalty method. Associated with the unilateral constraint, we obtain a multiplier \(\mu\) which is related to a measure dp. This measure is a positive Radon measure if G is continuous in all its arguments and is a finitely additive positive Radon measure if G is only measurable in the t-variable. We have indicated how the results of \textit{I. V. Girsanov} [see ''Lectures on mathematical theory of extremum problems'' (1972; Zbl 0234.49016)] follow from our results and how our results are related to those of \textit{K. Holmaker} [J. Optimization Theory Appl. 28, 391-410 (1979; Zbl 0387.49027)].
Mathematics Subject Classification ID: 49K35
Mathematics Subject Classification ID: 49J35
Mathematics Subject Classification ID: 49M30
zbMATH DE Number: 3951403
zbMATH Keywords: relaxed controls
zbMATH Keywords: penalty method
author: Negash G. Medhin
MaRDI profile type: Publication
cites work: A minimax optimal control problem
cites work: Lectures on mathematical theory of extremum problems. Translated from the Russian by D. Louvish
cites work: A penalty function proof of the maximum principle
cites work: Q5667133
cites work: Pontryagin's Maximum Principle and a Minimax Problem.
full work available at URL: https://doi.org/10.1007/bf00938465
OpenAlex ID: W1985714902
description: scientific article; zbMATH DE number 3951403