Nonlinear Schwarz preconditioning for nonlinear optimization problems with bound constraints
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866917583177908224 |
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| author | Kothari, Hardik Kopaničáková, Alena Krause, Rolf |
| author_facet | Kothari, Hardik Kopaničáková, Alena Krause, Rolf |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_14780 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Nonlinear Schwarz preconditioning for nonlinear optimization problems with bound constraints Kothari, Hardik Kopaničáková, Alena Krause, Rolf Optimization and Control Numerical Analysis 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. |
| title | Nonlinear Schwarz preconditioning for nonlinear optimization problems with bound constraints |
| topic | Optimization and Control Numerical Analysis |
| url | https://arxiv.org/abs/2211.14780 |