Nonlinear Schwarz preconditioning for nonlinear optimization problems with bound constraints

@article{Kothari2022NonlinearSP,
  title={Nonlinear Schwarz preconditioning for nonlinear optimization problems with bound constraints},
  author={Hardik Kothari and Alena Kopanivc'akov'a and Rolf H. Krause},
  journal={ArXiv},
  year={2022},
  volume={abs/2211.14780}
}
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 enhancedbyincorporating a solution-dependent coarse space, which takes into account the restricted constraints from the fine level. By means of… 
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