# Sufficient Conditions of Optimality for Control Pproblem Governed by Variational Inequalities

Serdica Mathematical Journal (1995)

- Volume: 21, Issue: 3, page 185-200
- ISSN: 1310-6600

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topNdoutoume, James. "Sufficient Conditions of Optimality for Control Pproblem Governed by Variational Inequalities." Serdica Mathematical Journal 21.3 (1995): 185-200. <http://eudml.org/doc/11666>.

@article{Ndoutoume1995,

abstract = {* 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.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.},

author = {Ndoutoume, James},

journal = {Serdica Mathematical Journal},

keywords = {Set-Valued Mapping; Proto-Derivative; Subgradient Operator; Pseudo-Convexity; Closed Convex Process; Optimality Condition; Variational Inequality; proto-derivative; subgradient operator; closed convex process; regularity assumption; set-valued mappings; variational inequalities; necessary conditions of optimality; weak pseudo-convexity},

language = {eng},

number = {3},

pages = {185-200},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Sufficient Conditions of Optimality for Control Pproblem Governed by Variational Inequalities},

url = {http://eudml.org/doc/11666},

volume = {21},

year = {1995},

}

TY - JOUR

AU - Ndoutoume, James

TI - Sufficient Conditions of Optimality for Control Pproblem Governed by Variational Inequalities

JO - Serdica Mathematical Journal

PY - 1995

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 21

IS - 3

SP - 185

EP - 200

AB - * 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.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.

LA - eng

KW - Set-Valued Mapping; Proto-Derivative; Subgradient Operator; Pseudo-Convexity; Closed Convex Process; Optimality Condition; Variational Inequality; proto-derivative; subgradient operator; closed convex process; regularity assumption; set-valued mappings; variational inequalities; necessary conditions of optimality; weak pseudo-convexity

UR - http://eudml.org/doc/11666

ER -

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