On Optimality Conditions in Control of Elliptic Variational Inequalities

Journal Article

Outrata Jiří, Jarušek Jiří, Stará J.

serial: Set-Valued and Variational Analysis vol.19, 1 (2011), p. 23-42

research: CEZ:AV0Z10750506

research: CEZ:AV0Z10190503

project(s): IAA100750802, GA AV ČR, GA201/09/0917, GA ČR

keywords: Directional differentiability, Critical cone, Strong local fuzzy sum rule, Calmness, Capacity

abstract (eng):

In the paper we consider optimal control of a class of strongly monotone variational inequalities, whose solution map is directionally differentiable in the control variable. This property is used to derive sharp pointwise necessary optimality conditions provided we do not impose any control or state constraints. In presence of such constraints we make use of the generalized differential calculus and derive, under a mild constraint qualification, optimality conditions in a “fuzzy” form. For strings, these conditions may serve as an intermediate step toward pointwise conditions of limiting (Mordukhovich) type and in the case of membranes they lead to a variant of Clarke stationarity conditions.

RIV: BA