Clarke’s Tangent cones, subgradients, optimality conditions, and the Lipschitzness at infinity - Nguyễn Minh Tùng (2024)
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.