On second-order weak sharp minima of general nonconvex set-constrained optimization problems
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866916847881814016 |
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| author | Ma, Xiaoxiao Ouyang, Wei Ye, Jane Zhang, Binbin |
| author_facet | Ma, Xiaoxiao Ouyang, Wei Ye, Jane Zhang, Binbin |
| contents | This paper explores local second-order weak sharp minima for a broad class of nonconvex optimization problems. We propose novel second-order optimality conditions formulated through the use of classical and lower generalized support functions. These results are based on asymptotic second-order tangent cones and outer second-order tangent sets. Specifically, our findings eliminate the necessity of assuming convexity in the constraint set and/or the outer second-order tangent set, or the nonemptiness of the outer second-order tangent set. Furthermore, unlike traditional approaches, our sufficient conditions do not rely on strong assumptions such as the uniform second-order regularity of the constraint set and the property of uniform approximation of the critical cones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12682 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On second-order weak sharp minima of general nonconvex set-constrained optimization problems Ma, Xiaoxiao Ouyang, Wei Ye, Jane Zhang, Binbin Optimization and Control This paper explores local second-order weak sharp minima for a broad class of nonconvex optimization problems. We propose novel second-order optimality conditions formulated through the use of classical and lower generalized support functions. These results are based on asymptotic second-order tangent cones and outer second-order tangent sets. Specifically, our findings eliminate the necessity of assuming convexity in the constraint set and/or the outer second-order tangent set, or the nonemptiness of the outer second-order tangent set. Furthermore, unlike traditional approaches, our sufficient conditions do not rely on strong assumptions such as the uniform second-order regularity of the constraint set and the property of uniform approximation of the critical cones. |
| title | On second-order weak sharp minima of general nonconvex set-constrained optimization problems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2507.12682 |