Minimax Theory and its Applications 09 (2024), No. 2, 157--170
Copyright Heldermann Verlag 2024
On the Convergence of Efficient Solutions to Semi-Infinite Set-Optimization 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 semi-infinite 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: Semi-infinite set optimization problem, stability, efficient solution, converse property, domination.
MSC: 49J53, 90C34, 90C31, 49J45.
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