Exploiting cone approximations in an augmented Lagrangian method for conic optimization
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866912334549614592 |
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| author | Fukuda, Mituhiro Gómez, Walter Haeser, Gabriel Mito, Leonardo Makoto |
| author_facet | Fukuda, Mituhiro Gómez, Walter Haeser, Gabriel Mito, Leonardo Makoto |
| contents | We propose an algorithm for general nonlinear conic programming which does not require the knowledge of the full cone, but rather a simpler, more tractable, approximation of it. We prove that the algorithm satisfies a strong global convergence property in the sense that it generates a strong sequential optimality condition. In particular, a KKT point is necessarily found when a limit point satisfies Robinson's condition. We conduct numerical experiments minimizing nonlinear functions subject to a copositive cone constraint. In order to do this, we consider a well known polyhedral approximation of this cone by means of refining the polyhedral constraints after each augmented Lagrangian iteration. We show that our strategy outperforms the standard approach of considering a close polyhedral approximation of the full copositive cone in every iteration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_00854 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exploiting cone approximations in an augmented Lagrangian method for conic optimization Fukuda, Mituhiro Gómez, Walter Haeser, Gabriel Mito, Leonardo Makoto Optimization and Control 90C30, 49M37, 90C26 We propose an algorithm for general nonlinear conic programming which does not require the knowledge of the full cone, but rather a simpler, more tractable, approximation of it. We prove that the algorithm satisfies a strong global convergence property in the sense that it generates a strong sequential optimality condition. In particular, a KKT point is necessarily found when a limit point satisfies Robinson's condition. We conduct numerical experiments minimizing nonlinear functions subject to a copositive cone constraint. In order to do this, we consider a well known polyhedral approximation of this cone by means of refining the polyhedral constraints after each augmented Lagrangian iteration. We show that our strategy outperforms the standard approach of considering a close polyhedral approximation of the full copositive cone in every iteration. |
| title | Exploiting cone approximations in an augmented Lagrangian method for conic optimization |
| topic | Optimization and Control 90C30, 49M37, 90C26 |
| url | https://arxiv.org/abs/2406.00854 |