Nonlinear Schwarz preconditioning for nonlinear optimization problems with bound constraints

Hardik Kothari; Alena Kopaničáková; Rolf Krause

doi:10.1007/978-3-031-50769-4_38

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arXiv · 2211.14780

Nonlinear Schwarz preconditioning for nonlinear optimization problems with bound constraints

Hardik Kothari·Alena Kopaničáková·Rolf Krause

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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.

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Hardik Kothari, Alena Kopaničáková, Rolf Krause. 2022-11-27. Nonlinear Schwarz preconditioning for nonlinear optimization problems with bound constraints. https://doi.org/10.1007/978-3-031-50769-4_38

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