Sufficient Conditions of Optimality for Control Pproblem Governed by Variational Inequalities

Ndoutoume, 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 -