Differentiation of operators and optimality conditions in category interpretation
type: Item
instance of: scholarly article
title: Differentiation of operators and optimality conditions in category interpretation
zbMATH Open document ID: 1215.49032
DOI: 10.3103/S1066369X10020076
author: S. Ya. Serovaiskii
published in: Russian Mathematics
publication date: 2010-02-19T00:00:00Z
review text: The author considers a system described by a nonlinear elliptic equation with large values of the nonlinearity parameter in which the domain dimension the control-state mapping is not Gâteaux differentiable. For this reason, one cannot immediately differentiate the optimality criterion and establish necessary optimality conditions by classical methods. Fortunately, the mentioned mapping is extendedly differentiable, allowing one to obtain in this way optimality conditions imposing no constraints on system parameters. An interpretation is also provided for the optimality conditions in terms of classical and extended derivatives within the theory of categories.
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 49K21
Mathematics Subject Classification ID: 18B99
Mathematics Subject Classification ID: 47N10
zbMATH DE Number: 5673451
zbMATH Keywords: optimality conditions
zbMATH Keywords: operator derivatives
zbMATH Keywords: nonlinear elliptic equation
zbMATH Keywords: categories
MaRDI profile type: Publication
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full work available at URL: s1066369x10020076
OpenAlex ID: W2076144825
description: scientific article; zbMATH DE number 5673451