Clarke’s Tangent Cones, Subgradients, Optimality Conditions, and the Lipschitzness at Infinity
Minh Tùng Nguyễn, Tiến-Sơn Phạm · SIAM Journal on Optimization · 2024
Abstract. We first study Clarke’s tangent cones at infinity to unbounded subsets of [Formula: see text]. 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 [Formula: see text] 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.