Clarke’s Tangent cones, subgradients, optimality conditions, and the Lipschitzness at infinity
We first study Clarke's tangent cones at infinity to unbounded subsets of \BbbR 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 \BbbR n and derive necessary optimality c...
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| Định dạng: | Journal article |
| Ngôn ngữ: | English |
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2024
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| Truy cập trực tuyến: | https://scholar.dlu.edu.vn/handle/123456789/3629 https://epubs.siam.org/doi/abs/10.1137/23M1545367 |
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oai:scholar.dlu.edu.vn:123456789-36292024-12-03T03:38:13Z Clarke’s Tangent cones, subgradients, optimality conditions, and the Lipschitzness at infinity Nguyễn Minh Tùng Phạm, Tiến Sơn tangent and normal cones, subgradients at infinity, optimality conditions, Lips- chitzness at infinity We first study Clarke's tangent cones at infinity to unbounded subsets of \BbbR 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 \BbbR 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 semicontinuous functions. 34 2 1732-1754 Khoa Toán – Tin 02 Phạm Tiến Sơn Danh mục Tạp chí ISI uy tín (Ban hành ngày 30/12/ 2021)/ 1921/53 2024-12-03T03:18:04Z 2024-12-03T03:18:04Z 2024-05 Journal article Bài báo đăng trên tạp chí thuộc ISI, bao gồm book chapter https://scholar.dlu.edu.vn/handle/123456789/3629 10.1137/23M1545367 https://epubs.siam.org/doi/abs/10.1137/23M1545367 en SIAM Journal on Optimization |
| institution |
Thư viện Trường Đại học Đà Lạt |
| collection |
Thư viện số |
| language |
English |
| topic |
tangent and normal cones, subgradients at infinity, optimality conditions, Lips- chitzness at infinity |
| spellingShingle |
tangent and normal cones, subgradients at infinity, optimality conditions, Lips- chitzness at infinity Nguyễn Minh Tùng Phạm, Tiến Sơn Clarke’s Tangent cones, subgradients, optimality conditions, and the Lipschitzness at infinity |
| description |
We first study Clarke's tangent cones at infinity to unbounded subsets of \BbbR 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 \BbbR 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 semicontinuous functions. |
| format |
Journal article |
| author |
Nguyễn Minh Tùng Phạm, Tiến Sơn |
| author_facet |
Nguyễn Minh Tùng Phạm, Tiến Sơn |
| author_sort |
Nguyễn Minh Tùng |
| title |
Clarke’s Tangent cones, subgradients, optimality conditions, and the Lipschitzness at infinity |
| title_short |
Clarke’s Tangent cones, subgradients, optimality conditions, and the Lipschitzness at infinity |
| title_full |
Clarke’s Tangent cones, subgradients, optimality conditions, and the Lipschitzness at infinity |
| title_fullStr |
Clarke’s Tangent cones, subgradients, optimality conditions, and the Lipschitzness at infinity |
| title_full_unstemmed |
Clarke’s Tangent cones, subgradients, optimality conditions, and the Lipschitzness at infinity |
| title_sort |
clarke’s tangent cones, subgradients, optimality conditions, and the lipschitzness at infinity |
| publishDate |
2024 |
| url |
https://scholar.dlu.edu.vn/handle/123456789/3629 https://epubs.siam.org/doi/abs/10.1137/23M1545367 |
| _version_ |
1817660465668423680 |