Gamkrelidze convexification and Bogolyubov's theorem
type: Item
instance of: scholarly article
title: Gamkrelidze convexification and Bogolyubov's theorem
zbMATH Open document ID: 1442.49039
DOI: 10.1134/S0001434620030219
published in: Mathematical Notes
publication date: 2020-06-26T00:00:00Z
review text: This work is dedicated to studying the so-called ``interconnection'' between an optimal control problem and its convexification in the sense of Gamkrelidze and Bogolyubov, by means of biconjugate functions, as a sort of counterpart to the classical Fenchel-Moreau theorem from convex analysis. As a special case of the main statement, the authors rediscover Bogolyubov's classical similar result concerning variational calculus problems. Some examples illustrate the theoretical achievements.
reviewed by: Sorin-Mihai Grad
Mathematics Subject Classification ID: 49N05
Mathematics Subject Classification ID: 49N15
Mathematics Subject Classification ID: 49J15
Mathematics Subject Classification ID: 49K15
zbMATH DE Number: 7215384
zbMATH Keywords: optimal control problem
zbMATH Keywords: second conjugate function
zbMATH Keywords: convexification
author: E. R. Avakov
author: G. G. Magaril-Il'yaev
MaRDI profile type: Publication
cites work: Q5340325
cites work: Q3663911
cites work: Local infimum and a family of maximum principles in optimal control
full work available at URL: s0001434620030219
OpenAlex ID: W3019215119
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description: scientific article