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- Title
SOLVABILITY OF CONVEX OPTIMIZATION PROBLEMS ON A ∗-CONTINUOUS CLOSED CONVEX SET.
- Authors
XI YIN ZHENG
- Abstract
Given a closed convex set A in a Banach space X, motivated by the continuity of A [Gale and Klee, Math. Scand. 7 (1959), 379-391], this paper introduces and studies the ∗-continuity of A. Without the reflexivity assumption on X, we prove that the ∗-continuity of a closed convex set A implies that, for every continuous linear (or convex) function f : X → R bounded below on A, the corresponding optimization problem infx∈A f(x) is weakly well-posed solvable, and that A has the attainable separation property if A is assumed to have a nonempty interior in addition.
- Subjects
CONVEX functions; CONSTRAINED optimization; SET theory; TOPOLOGY; BANACH spaces; GENERALIZATION
- Publication
Journal of Applied & Numerical Optimization, 2022, Vol 4, Issue 1, p119
- ISSN
2562-5527
- Publication type
Article
- DOI
10.23952/jano.4.2022.1.09