Regularity properties of optimal controls with application to discrete approximation
type: Item
instance of: scholarly article
title: Regularity properties of optimal controls with application to discrete approximation
zbMATH Open document ID: 0956.49018
DOI: 10.1023/A:1021842412255
published in: Journal of Optimization Theory and Applications
publication date: 2000-06-27T00:00:00Z
review text: The paper is an improvement of the recent result of \textit{A. L. Dontchev} [SIAM J. Control Optimization 34, No. 4, 1315-1328 (1996; Zbl 0851.49023)] about discrete approximations under uniform coercivity conditions on the discrete solutions for differential equations. Moreover, the regularity is further specified by Lipschitz continuity. The form of \( L_{\infty}\)-terms for the optimal control problem is proceeding along the essential limit concept for \(L_{\infty}\)-functions (Section 2) and the description of structure of an optimal control based on a finite number of Lipschitz continuous arcs (Section 3). The final section is devoted to the above mentioned improvement and discussions about the expected convergence properties of the Euler approximation with jump discontinuities located at resident grid points w.r.t. the sequence of discretizations.
Mathematics Subject Classification ID: 49M25
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 49K15
Mathematics Subject Classification ID: 49N60
zbMATH DE Number: 1347772
zbMATH Keywords: optimal control
zbMATH Keywords: discrete approximation
zbMATH Keywords: Lipschitz continuity
zbMATH Keywords: coercivity condition
zbMATH Keywords: solution regularity
author: Ursula Felgenhauer
MaRDI profile type: Publication
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full work available at URL: a:1021842412255
OpenAlex ID: W42018447
description: scientific article; zbMATH DE number 1347772