Clarke's tangent cones, subgradients, optimality conditions and the Lipschitzness at infinity
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866910448618569728 |
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| author | Nguyen, Minh Tung Pham, Tien-Son |
| author_facet | Nguyen, Minh Tung Pham, Tien-Son |
| contents | We first study Clarke's tangent cones at infinity to unbounded subsets of $\mathbb{R}^n.$ We prove that these cones are closed convex and show a characterization of their interiors. We then study subgradients at infinity for extended real value functions on $\mathbb{R}^n$ and derive necessary optimality conditions at infinity for optimization problems. We also give a number of rules for the computing of subgradients at infinity and provide some characterizations of the Lipschitz continuity at infinity for lower semi-continuous functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_08677 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Clarke's tangent cones, subgradients, optimality conditions and the Lipschitzness at infinity Nguyen, Minh Tung Pham, Tien-Son Optimization and Control Classical Analysis and ODEs 90C30, 90C46, 49J52, 49J53 We first study Clarke's tangent cones at infinity to unbounded subsets of $\mathbb{R}^n.$ We prove that these cones are closed convex and show a characterization of their interiors. We then study subgradients at infinity for extended real value functions on $\mathbb{R}^n$ and derive necessary optimality conditions at infinity for optimization problems. We also give a number of rules for the computing of subgradients at infinity and provide some characterizations of the Lipschitz continuity at infinity for lower semi-continuous functions. |
| title | Clarke's tangent cones, subgradients, optimality conditions and the Lipschitzness at infinity |
| topic | Optimization and Control Classical Analysis and ODEs 90C30, 90C46, 49J52, 49J53 |
| url | https://arxiv.org/abs/2211.08677 |