Preconditioned Conjugate Gradient Method for Optimal Control Problems with Control and State Constraints

Optimality systems and their linearizations arising in optimal control of partial differential equations with pointwise control and (regularized) state constraints are considered. The preconditioned conjugate gradient (pcg) method in a non-standard inner product is employed for their efficient solution. Preconditioned condition numbers are estimated for problems with pointwise control constraints, mixed control-state constraints, and of Moreau-Yosida penalty type. Numerical results for elliptic problems demonstrate the performance of the pcg iteration. Regularized stateconstrained problems in 3D with more than 750,000 variables are solved. Key words. preconditioned conjugate gradient method, saddle point problems, optimal control of PDEs, control and state constraints, multigrid method AMS subject classifications. 49K20, 49M15, 65F08, 65N55

• Type: Journal
• Year: 2010
• Where: SIAMMAX
• Authors: Roland Herzog, Ekkehard W. Sachs
• Keywords: Pointwise Control, Preconditioned Conjugate, SIAMMAX 2010, State Constraints