New second-order optimality conditions for directional optimality of a general set-constrained optimization problem
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910852440915968 |
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| author | Ouyang, Wei Ye, Jane Zhang, Binbin |
| author_facet | Ouyang, Wei Ye, Jane Zhang, Binbin |
| contents | In this paper we derive new second-order optimality conditions for a very general set-constrained optimization problem where the underlying set may be nononvex. We consider local optimality in specific directions (i.e., optimal in a directional neighborhood) in pursuit of developing these new optimality conditions. First-order necessary conditions for local optimality in given directions are provided by virtue of the corresponding directional normal cones. Utilizing the classical and/or the lower generalized support function, we obtain new second-order necessary and sufficient conditions for local optimality of general nonconvex constrained optimization problem in given directions via both the corresponding asymptotic second-order tangent cone and outer second-order tangent set. Our results do not require convexity and/or nonemptyness of the outer second-order tangent set. This is an important improvement to other results in the literature since the outer second-order tangent set can be nonconvex and empty even when the set is convex. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17696 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New second-order optimality conditions for directional optimality of a general set-constrained optimization problem Ouyang, Wei Ye, Jane Zhang, Binbin Optimization and Control In this paper we derive new second-order optimality conditions for a very general set-constrained optimization problem where the underlying set may be nononvex. We consider local optimality in specific directions (i.e., optimal in a directional neighborhood) in pursuit of developing these new optimality conditions. First-order necessary conditions for local optimality in given directions are provided by virtue of the corresponding directional normal cones. Utilizing the classical and/or the lower generalized support function, we obtain new second-order necessary and sufficient conditions for local optimality of general nonconvex constrained optimization problem in given directions via both the corresponding asymptotic second-order tangent cone and outer second-order tangent set. Our results do not require convexity and/or nonemptyness of the outer second-order tangent set. This is an important improvement to other results in the literature since the outer second-order tangent set can be nonconvex and empty even when the set is convex. |
| title | New second-order optimality conditions for directional optimality of a general set-constrained optimization problem |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2404.17696 |