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Volume 21 Number 3 >

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Title: Sufficient Conditions of Optimality for Control Pproblem Governed by Variational Inequalities
Authors: Ndoutoume, James
Keywords: Set-Valued Mapping
Subgradient Operator
Closed Convex Process
Optimality Condition
Variational Inequality
Issue Date: 1995
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 21, No 3, (1995), 185p-200p
Abstract: The author recently introduced a regularity assumption for derivatives of set-valued mappings, in order to obtain first order necessary conditions of optimality, in some generalized sense, for nondifferentiable control problems governed by variational inequalities. It was noticed that this regularity assumption can be viewed as a symmetry condition playing a role parallel to that of the wellknown symmetry property of the Hessian of a function at a given point. In this paper, we elaborate this point in a more detailed way and discuss some related questions. The main issue of the paper is to show (using this symmetry condition) that necessary conditions of optimality alluded above can be shown to be also sufficient if a weak pseudo-convexity assumption is made for the subgradient operator governing the control equation. Some examples of application to concrete situations are presented involving obstacle problems.
Description: * This work was completed while the author was visiting the University of Limoges. Support from the laboratoire “Analyse non-linéaire et Optimisation” is gratefully acknowledged.
ISSN: 1310-6600
Appears in Collections:Volume 21 Number 3

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