On Optimality Conditions in Control of Elliptic Variational Inequalities |
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Authors: | Ji?í Outrata Ji?í Jaru?ek Jana Stará |
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Institution: | 1.Institute of Information Theory and Automation,Academy of Sciences of the Czech Republic,Praha 8,Czech Republic;2.Institute of Mathematics,Academy of Sciences of the Czech Republic,Praha 1,Czech Republic;3.Department of Mathematical Analysis, Faculty of Mathematics and Physics,Charles University,Praha 8,Czech Republic |
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Abstract: | 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. |
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Keywords: | |
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