Tin tức nổi bật
Hội thảo sắp diễn ra
THE 3RD VIETNAM - KOREA JOINT WORKSHOP ON SELECTED TOPICS IN MATHEMATICS
International conference on commutative algebra to the memory of Jürgen Herzog
Xuất bản mới
Approximate Proper Efficiency in Vector Optimization via Benson's Approach (tiếp theo)
Người báo cáo: Nguyễn Thị Thu Hương (Học viện Kỹ thuật Quân sự)
Thời gian: 9h00 đến 11h00 sáng thứ 4 ngày 24.01.2024
Địa điểm: Phòng 302 nhà A5 Viện Toán học.
Tóm tắt: We present two criteria for checking approximate proper efficiency in vector optimization problems with the ordering cone being a nonnegative orthant. Although the criteria can be established by Benson's approach [H.P. Benson, textit{An improved definition of proper efficiency for vector maximization with respect to cones}, J. Math. Anal. Appl. textbf{71} (1979), 232--241], detailed proofs are given for the first time here. The two criteria are strong motivations to introduce the concept of $e$-properly efficient solution, where $e$ is any nonzero vector taken from the closed pointed convex ordering cone. For an arbitrary linear vector optimization problem, we show that either the $e$-properly efficient solution set is empty or it coincides with the $e$-efficient solution set. This new result has no analogue in the literature