
Minimax Theory and its Applications 09 (2024), No. 2, 157170 Copyright Heldermann Verlag 2024 On the Convergence of Efficient Solutions to SemiInfinite SetOptimization Problems Lam Quoc Anh Department of Mathematics, Teacher College, Can Tho University, Can Tho, Vietnam quocanh@ctu.edu.vn Lam Van Day Department of Mathematics, Nam Can Tho University, Can Tho, Vietnam lvday@nctu.edu.vn Tran Quoc Duy Department of Mathematics, FPT University, Can Tho, Vietnam duytq4@fe.edu.vn We consider semiinfinite set optimization problems and study the stability of efficient solutions for such problems. We first discuss upper and lower semicontinuity properties of the constraint sets. Next, we introduce a concept of converse property for the original problem and employ it to establish the upper convergence for efficient solutions. Besides, we also propose concepts of sequential domination to consider the lower convergence for efficient solutions. Keywords: Semiinfinite set optimization problem, stability, efficient solution, converse property, domination. MSC: 49J53, 90C34, 90C31, 49J45. [ Fulltextpdf (134 KB)] for subscribers only. 