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Volume 4, Issue 1, 1 April 2022, Pages 119-128
Abstract. Given a closed convex set A in a Banach space X, motivated by the continuity of A [D. Gale, V. Klee, Continuous convex sets, 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 bounded below on A, the corresponding optimization problem is weakly well-posed solvable, and that A has the attainable separation property if A is assumed to have a nonempty interior in addition.
How to Cite this Article:
Xi-Yin Zheng, Solvability of convex optimization problems on a *-continuous closed convex set, J. Appl. Numer. Optim. 4 (2022), 119-128.