Generalized derivatives for the solution operator of the obstacle\n problem

2018/06/13 by Anne-Therese Rauls, Gerd Wachsmuth, Rauls, Anne-Therese +1
Computer Science · Engineering · #47J20 #49J52 #49K40 #58C20 #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Optimization and Variational Analysis #Stability and Control of Uncertain Systems

paper · pdf · doi:10.48550/arxiv.1806.05052

openalex publication_date 2018/06/13 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

We characterize generalized derivatives of the solution operator of the\nobstacle problem. This precise characterization requires the usage of the\ntheory of so-called capacitary measures and the associated solution operators\nof relaxed Dirichlet problems. The generalized derivatives can be used to\nobtain a novel necessary optimality condition for the optimal control of the\nobstacle problem with control constraints. A comparison shows that this system\nis stronger than the known system of C-stationarity.\n

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