Nonlinear Derivative-free Constrained Optimization with a Penalty-Interior Point Method and Direct Search
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915733181562880 |
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| author | Brilli, Andrea Custódio, Ana L. Liuzzi, Giampaolo Silva, Everton J. |
| author_facet | Brilli, Andrea Custódio, Ana L. Liuzzi, Giampaolo Silva, Everton J. |
| contents | In this work, the joint use of a mixed penalty-interior point method and direct search is proposed, to address {nonlinear} constrained derivative-free optimization problems. A merit function is considered, wherein the set of nonlinear inequality constraints is divided into two groups: one treated with a logarithmic barrier approach, and another, along with the equality constraints, addressed using a penalization term. This strategy is adapted and incorporated into a direct search method, enabling the effective handling of general nonlinear constraints. Convergence to KKT-stationary points is established under continuous differentiability assumptions, without requiring any kind of convexity. Computational experiments on analytical problems and an engineering application demonstrate the robustness, efficiency, and overall effectiveness of the proposed method, when compared with state-of-the-art solvers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_21634 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonlinear Derivative-free Constrained Optimization with a Penalty-Interior Point Method and Direct Search Brilli, Andrea Custódio, Ana L. Liuzzi, Giampaolo Silva, Everton J. Optimization and Control 65K05, 90C30, 90C56 In this work, the joint use of a mixed penalty-interior point method and direct search is proposed, to address {nonlinear} constrained derivative-free optimization problems. A merit function is considered, wherein the set of nonlinear inequality constraints is divided into two groups: one treated with a logarithmic barrier approach, and another, along with the equality constraints, addressed using a penalization term. This strategy is adapted and incorporated into a direct search method, enabling the effective handling of general nonlinear constraints. Convergence to KKT-stationary points is established under continuous differentiability assumptions, without requiring any kind of convexity. Computational experiments on analytical problems and an engineering application demonstrate the robustness, efficiency, and overall effectiveness of the proposed method, when compared with state-of-the-art solvers. |
| title | Nonlinear Derivative-free Constrained Optimization with a Penalty-Interior Point Method and Direct Search |
| topic | Optimization and Control 65K05, 90C30, 90C56 |
| url | https://arxiv.org/abs/2407.21634 |