Preconditioners for state-constrained optimal control problems with Moreau-Yosida penalty function

• Published in: Numerical linear algebra with applications Vol. 21; no. 1; pp. 81 - 97
• Main Authors: Pearson, John W., Stoll, Martin, Wathen, Andrew J.
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01-01-2014; Wiley Subscription Services, Inc
• Subjects: Inclusions; Krylov subspace solver; Linear algebra; Mathematical models; Newton method; Optimal control; Optimization; Partial differential equations; PDE-constrained optimization; preconditioning; Regularization; saddle point systems; State variable; state-constrained problems
• ISSN: 1070-5325; 1099-1506
• DOI: 10.1002/nla.1863

SUMMARYOptimal control problems with partial differential equations as constraints play an important role in many applications. The inclusion of bound constraints for the state variable poses a significant challenge for optimization methods. Our focus here is on the incorporation of the constraints via the Moreau–Yosida regularization technique. This method has been studied recently and has proven to be advantageous compared with other approaches. In this paper, we develop robust preconditioners for the efficient solution of the Newton steps associated with the fast solution of the Moreau–Yosida regularized problem. Numerical results illustrate the efficiency of our approach. Copyright © 2012 John Wiley & Sons, Ltd.