Nonlinear Schwarz preconditioning for nonlinear optimization problems with bound constraints
Optimization and Control
2024-02-07 v1 Numerical Analysis
Numerical Analysis
Abstract
We propose a nonlinear additive Schwarz method for solving nonlinear optimization problems with bound constraints. Our method is used as a "right-preconditioner" for solving the first-order optimality system arising within the sequential quadratic programming (SQP) framework using Newton's method. The algorithmic scalability of this preconditioner is enhanced by incorporating a solution-dependent coarse space, which takes into account the restricted constraints from the fine level. By means of numerical examples, we demonstrate that the proposed preconditioned Newton methods outperform standard active-set methods considered in the literature.
Cite
@article{arxiv.2211.14780,
title = {Nonlinear Schwarz preconditioning for nonlinear optimization problems with bound constraints},
author = {Hardik Kothari and Alena Kopaničáková and Rolf Krause},
journal= {arXiv preprint arXiv:2211.14780},
year = {2024}
}