A globalized inexact semismooth Newton method for strongly convex optimal control problems
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915901980278784 |
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| author | Wachsmuth, Daniel |
| author_facet | Wachsmuth, Daniel |
| contents | We investigate a globalized inexact semismooth Newton method applied to strongly convex optimization problems in Hilbert spaces. Here, the semismooth Newton method is appplied to the dual problem, which has a continuously differentiable objective. We prove global strong convergence of iterates as well as transition to local superlinear convergence. The latter needs a second-order Taylor expansion involving semismooth derivative concepts. The convergence of the globalized method is demonstrated in numerical examples, for which the local unglobalized method diverges. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21612 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A globalized inexact semismooth Newton method for strongly convex optimal control problems Wachsmuth, Daniel Optimization and Control We investigate a globalized inexact semismooth Newton method applied to strongly convex optimization problems in Hilbert spaces. Here, the semismooth Newton method is appplied to the dual problem, which has a continuously differentiable objective. We prove global strong convergence of iterates as well as transition to local superlinear convergence. The latter needs a second-order Taylor expansion involving semismooth derivative concepts. The convergence of the globalized method is demonstrated in numerical examples, for which the local unglobalized method diverges. |
| title | A globalized inexact semismooth Newton method for strongly convex optimal control problems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2503.21612 |