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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Autors principals: Nguyễn Minh Tùng, Phạm, Tiến Sơn
Format: Journal article
Idioma:English
Publicat: 2024
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Accés en línia:https://scholar.dlu.edu.vn/handle/123456789/3629
https://epubs.siam.org/doi/abs/10.1137/23M1545367
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Sumari: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.