Multigrid Solution of a Lavrentiev-Regularized State-Constrained Parabolic Control Problem

作者：Borzi Alfio^*; Gonzalez Andrade Sergio

来源：Numerical Mathematics: Theory, Methods and Applications , 2012, 5(1): 1-18.

DOI：10.4208/nmtma.2011.m12si01

• Multigrid methods
• Lavrentiev regularization
• semismooth Newton methods
• parabolic partial differential equations
• optimal control theory

A mesh-independent, robust, and accurate multigrid scheme to solve a linear state-constrained parabolic optimal control problem is presented. We first consider a Lavrentiev regularization of the state-constrained optimization problem. Then, a multigrid scheme is designed for the numerical solution of the regularized optimality system. Central to this scheme is the construction of an iterative pointwise smoother which can be formulated as a local semismooth Newton iteration. Results of numerical experiments and theoretical twogrid local Fourier analysis estimates demonstrate that the proposed scheme is able to solve parabolic state-constrained optimality systems with textbook multigrid efficiency.

• 出版日期2012-2