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A fast solver for an H1 regularized PDE-constrained optimization problem. (English) Zbl 1373.49028
Summary: We consider PDE-constrained optimization problems which incorporate an H1 regularization control term. We focus on a time-dependent PDE, and consider both distributed and boundary control. The problems we consider include bound constraints on the state, and we use a Moreau-Yosida penalty function to handle this. We propose Krylov solvers and Schur complement preconditioning strategies for the different problems and illustrate their performance with numerical examples.

MSC:
49M25 Discrete approximations in optimal control
49K20 Optimality conditions for problems involving partial differential equations
65K10 Numerical optimization and variational techniques
65F10 Iterative numerical methods for linear systems
65F50 Computational methods for sparse matrices
65M22 Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs
65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
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