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arXiv · 2211.08677

Clarke's tangent cones, subgradients, optimality conditions and the Lipschitzness at infinity

Minh Tung Nguyen·Tien-Son Pham
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Abstract

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.

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Minh Tung Nguyen, Tien-Son Pham. 2022-11-16. Clarke's tangent cones, subgradients, optimality conditions and the Lipschitzness at infinity. https://arxiv.org/abs/2211.08677

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