2021/12/13 by Eduardo Casas, Karl Kunisch, Casas, Eduardo +1
Computer Science · Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Nonlinear Partial Differential Equations #Optimization and Variational Analysis #math.OC #msc:35K58 #msc:49J20 #msc:49J52 #msc:49K20
paper · pdf · doi:10.48550/arxiv.2112.06535
arxiv created 2021/12/13 · arxiv updated 2021/12/14
Infinite horizon open loop optimal control problems for semilinear parabolic equations are investigated. The controls are subject to a cost-functional which promotes sparsity in time. The focus is put on deriving first order optimality conditions. This is achieved without relying on a well-defined control-to-state mapping in a neighborhood of minimizers. The technique of proof is based on the approximation of the original problem by a family of finite horizon problems. The optimality conditions allow to deduce sparsity properties of the optimal controls in time.