First-order conditions for the optimal control of the obstacle problem\n with state constraints

2020/12/30 by Ira Neitzel, Gerd Wachsmuth, Neitzel, Ira +1
Computer Science · Engineering · #35J86 #49K21 #FOS: Mathematics #Guidance and Control Systems #Optimization and Control (math.OC) #Optimization and Variational Analysis #Spacecraft Dynamics and Control

paper · pdf · doi:10.48550/arxiv.2012.15324

openalex publication_date 2020/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider an optimal control problem in which the state is governed by an\nunilateral obstacle problem (with obstacle from below) and restricted by a\npointwise state constraint (from above). In the presence of control\nconstraints, we prove, via regularization of the state constraints, that a\nsystem of C-stationarity is necessary for optimality. In the absence of control\nconstraints, we show that local minimizers are even strongly stationary by a\ncareful discussion of the primal first-order conditions of B-stationary type.\n

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