Convergence analysis of the semismooth Newton method for sparse control problems governed by semilinear elliptic equations
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916807790559232 |
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| author | Eduardo, Casas Mariano, Mateos |
| author_facet | Eduardo, Casas Mariano, Mateos |
| contents | We show that a second order sufficient condition for local optimality, along with a strict complementarity condition, is enough to get the superlinear convergence of the semismooth Newton method for an optimal control problem governed by a semilinear elliptic equation. The objective functional may include a sparsity promoting term and we allow for box control constraints. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_05393 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Convergence analysis of the semismooth Newton method for sparse control problems governed by semilinear elliptic equations Eduardo, Casas Mariano, Mateos Optimization and Control 35J61, 49K20, 49M15, 49M05 We show that a second order sufficient condition for local optimality, along with a strict complementarity condition, is enough to get the superlinear convergence of the semismooth Newton method for an optimal control problem governed by a semilinear elliptic equation. The objective functional may include a sparsity promoting term and we allow for box control constraints. |
| title | Convergence analysis of the semismooth Newton method for sparse control problems governed by semilinear elliptic equations |
| topic | Optimization and Control 35J61, 49K20, 49M15, 49M05 |
| url | https://arxiv.org/abs/2309.05393 |