A semi-smooth Newton method for the nonlinear conic problem with generalized simplicial cones
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908982433546240 |
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| author | Armijo, Nicolas F. Cruz, Yunier Bello Haeser, Gabriel |
| author_facet | Armijo, Nicolas F. Cruz, Yunier Bello Haeser, Gabriel |
| contents | In this work we develop and analyze a semi-smooth Newton method for the general nonlinear conic programming problem. In particular, we study the problem with a generalized simplicial cone, i.e., the image of a symmetric cone under a linear mapping. We generalize Robinson's normal equations to a conic setting, yielding what we call the conic projection equations. The resulting system is equivalent to the KKT conditions associated with the nonlinear conic programming problem. A semi-smooth Newton iteration is proposed for solving it, and local quadratic convergence is established. We study properties of generalized simplicial cones and prove strong semi-smoothness of the projection operator onto them. Numerical experiments compare the method against a recent smoothing Newton approach on the circular cone programming problem, and we also apply it to the low-rank matrix completion problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_18858 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A semi-smooth Newton method for the nonlinear conic problem with generalized simplicial cones Armijo, Nicolas F. Cruz, Yunier Bello Haeser, Gabriel Optimization and Control In this work we develop and analyze a semi-smooth Newton method for the general nonlinear conic programming problem. In particular, we study the problem with a generalized simplicial cone, i.e., the image of a symmetric cone under a linear mapping. We generalize Robinson's normal equations to a conic setting, yielding what we call the conic projection equations. The resulting system is equivalent to the KKT conditions associated with the nonlinear conic programming problem. A semi-smooth Newton iteration is proposed for solving it, and local quadratic convergence is established. We study properties of generalized simplicial cones and prove strong semi-smoothness of the projection operator onto them. Numerical experiments compare the method against a recent smoothing Newton approach on the circular cone programming problem, and we also apply it to the low-rank matrix completion problem. |
| title | A semi-smooth Newton method for the nonlinear conic problem with generalized simplicial cones |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2604.18858 |