0356042 20240103194817.020110208235959.9 000286832900002 10.1007/s11228-010-0158-4 20 s. cav_un_epca*03439671877-0533191 (2011)23-42Springer Directional differentiability Critical cone Strong local fuzzy sum rule Calmness Capacity cav_un_auth*0101173 Outrata Jiří Matematická teorie rozhodování Department of Decision Making Theory MTR MTR UTIA-B Department of Decision Making Theory Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0100666 Jarušek Jiří Evoluční diferenciální rovnice Evolution Differential Equations EDE MU-W Evolution Differential Equations Matematický ústav AV ČR, v. v. i. cav_un_auth*0045840 Stará J. CZ IAA100750802 GA AV ČR cav_un_auth*0241214 GA201/09/0917 GA ČR cav_un_auth*0254029 CEZ:AV0Z10750506 CEZ:AV0Z10190503 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. 2011 BA 4 R 4r 20231122134435.7 http://hdl.handle.net/11104/0194666 MATHEMATICSAPPLIED 0.791 0.067 0.00052 0.661 37 30 1.417 Q1 55.047 56.122 Q2 Q2 2011 Soubory v repozitáři: Jarusek2.pdf 000286832900002 WOS cav_un_epca*0343967 Set-Valued and Variational Analysis 1877-0533 1877-0541 Roč. 19 č. 1 2011 23 42 Springer