Minimax Theory and its Applications 09 (2024), No. 1, 117--128
Copyright Heldermann Verlag 2024
Optimal Control of Stochastic Variational Inequalities
Wilfried Grecksch
Institute of Mathematics, Martin-Luther-University, Halle-Wittenberg, Germany
wilfried.grecksch@mathematik.uni-halle.de
Akhtar A. Khan
School of Mathematical Sciences, Rochester Inst. of Technology, Rochester, New York, U.S.A.
aaksma@rit.edu
Miguel Sama
Dept. de Matemática Aplicada, Universidad Nacional de Educación a Distancia, Madrid, Spain
msama@ind.uned.es
Christiane Tammer
Institute of Mathematics, Martin-Luther-University, Halle-Wittenberg, Germany
christiane.tammer@mathematik.uni-halle.de
This work focuses on the optimal control problem for elliptic stochastic variational inequalities where the diffusivity coefficient and the source term are random fields. Besides recalling the existence theorem for the stochastic elliptic variational inequalities, we also give an existence result for the optimal control problem, which is posed as a stochastic optimization problem. We conduct two preliminary computational experiments by coupling the penalty method with the stochastic approximation approach.
Keywords: Stochastic optimal control, partial differential equations with random data, stochastic approximation, regularization, penalization.
MSC: 35R30, 49N45, 65J20, 65J22, 65M30.
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