Premium
Preconditioners for state‐constrained optimal control problems with Moreau–Yosida penalty function
Author(s) -
Pearson John W.,
Stoll Martin,
Wathen Andrew J.
Publication year - 2014
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.1863
Subject(s) - regularization (linguistics) , mathematics , optimal control , mathematical optimization , penalty method , focus (optics) , state variable , state (computer science) , function (biology) , computer science , algorithm , evolutionary biology , biology , physics , artificial intelligence , optics , thermodynamics
SUMMARY Optimal 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.