Multigrid methods for saddle point problems: Karush-Kuhn-Tucker systems
arXiv:1811.124341 citationsh-index: 42
Originality Incremental advance
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Provides robust solvers for PDE-constrained optimization problems, which are important for scientific computing applications.
Developed multigrid methods for elliptic distributed optimal control problems that are robust with respect to the regularization parameter, proving uniform convergence of the W-cycle and demonstrating performance in 2D and 3D numerical experiments.
We construct multigrid methods for an elliptic distributed optimal control problem that are robust with respect to a regularization parameter. We prove the uniform convergence of the $W$-cycle algorithm and demonstrate the performance of $V$-cycle and $W$-cycle algorithms in two and three dimensions through numerical experiments.