# Nonlinear Schwarz preconditioning for nonlinear optimization problems with bound constraints

arXiv: https://arxiv.org/abs/2211.14780 · HTML: https://mlsanity.com/paper/2211.14780/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Nov 2022.

## Built on by (most cited first, 3 of 3)

- [Enhancing training of physics-informed neural networks using domain-decomposition based preconditioning strategies](https://mlsanity.com/paper/2306.17648/) (2023)
- [Two-level overlapping additive Schwarz preconditioner for training scientific machine learning applications](https://mlsanity.com/paper/2406.10997/) (2024)
- [Recursive Bound-Constrained AdaGrad with Applications to Multilevel and Domain Decomposition Minimization](https://mlsanity.com/paper/2507.11513/) (2025)

## Abstract (arXiv)

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.