2014/07/04 by Margherita Porcelli, Valeria Simoncini, Porcelli, Margherita +3 · 1 citation
Computer Science · Engineering · Mathematics · #15A09 #65F50 #65K05 #Advanced Numerical Methods in Computational Mathematics #Advanced Optimization Algorithms Research #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1407.1144
openalex publication_date 2014/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We address the problem of preconditioning a sequence of saddle point linear systems arising in the solution of PDE-constrained optimal control problems via active-set Newton methods, with control and (regularized) state constraints. We present two new preconditioners based on a full block matrix factorization of the Schur complement of the Jacobian matrices, where the active-set blocks are merged into the constraint blocks. We discuss the robustness of the new preconditioners with respect to the parameters of the continuous and discrete problems. Numerical experiments on 3D problems are presented, including comparisons with existing approaches based on preconditioned conjugate gradients in a nonstandard inner product.