Lê Thanh Tùng * , Phạm Thanh Hùng , Trần Thiện Khải Phạm Lê Bạch Ngọc

* Tác giả liên hệ (lttung@ctu.edu.vn)

Abstract

This paper is to deal with Mond-Weir duality and Wolfe duality for constrained set-valued optimization problems in terms of cone-directed Clarke derivatives. Firstly, necessary and sufficient optimality conditions for constrained set-valued optimizations in terms of cone-directed Clarke derivatives for the cone-semilocally convex like maps are investigated. Then, the Mond-Weir duality and Wolfe duality for a constrained set-valued optimization and their weak duality, strong duality and converse duality are considered.
Keywords: Cone-directed Clarke derivatives, Mond-Weir duality, Optimality conditions, Set-valued optimization, Wolfe duality

Tóm tắt

Bài báo này khảo sát bài toán đối ngẫu dạng Mond-Weir và Wolfe cho bài toán tối ưu đa trị có ràng buộc sử dụng đạo hàm đa trị Clarke theo hướng nón. Trước hết, điều kiện tối ưu cần và đủ cho bài toán tối ưu đa trị có ràng buộc sử dụng đạo hàm đa trị Clarke theo hướng nón cho lớp hàm tựa lồi nửa địa phương được khảo sát. Sau đó, bài toán đối ngẫu dạng Mond-Weir và Wolfe cho bài toán tối ưu đa trị có ràng buộc và các tính chất về đối ngẫu mạnh, đối ngẫu yếu và đối ngẫu ngược được trình bày.
Từ khóa: Bài toán tối ưu đa trị, các điều kiện tối ưu, đạo hàm Clarke theo hướng nón, đối ngẫu Mond-Weir, đối ngẫu Wolfe

Article Details

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