On Optimality Conditions in Control of Elliptic Variational Inequalities

0356042 - ÚTIA 2011 RIV NL eng J - Journal Article
Outrata, Jiří - Jarušek, Jiří - Stará, J.
On Optimality Conditions in Control of Elliptic Variational Inequalities.
Set-Valued and Variational Analysis. Roč. 19, č. 1 (2011), s. 23-42. ISSN 1877-0533. E-ISSN 1877-0541
R&D Projects: GA AV ČR IAA100750802; GA ČR GA201/09/0917
Institutional research plan: CEZ:AV0Z10750506; CEZ:AV0Z10190503
Keywords : Directional differentiability * Critical cone * Strong local fuzzy sum rule * Calmness * Capacity
Subject RIV: BA - General Mathematics
Impact factor: 0.791, year: 2011

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.
Permanent Link: http://hdl.handle.net/11104/0194666