Lam Quoc Anh , Pham Thanh Duoc , Vo Thi Mong Thuy * and Dang Thi My Van

* Corresponding author (vtmthuy@tdu.edu.vn)

Abstract

This paper focuses on studying parametric vector optimization problems via improvement sets and investigating the Hausdorff continuity of weakly efficient solution mappings of these problems. Firstly, properties of improvement sets are discussed. Then, models of parametric vector optimization problems via improvement sets and their weakly efficient solutions are introduced. Finally, by using the properties of improvement sets and convexity conditions of a vector-valued mapping, sufficient conditions for the Hausdorff continuity of these weak efficient solution mappings are investigated.

Keywords: Hausdorff continuity, improvement set, vector optimization problem, weakly efficient solution

Tóm tắt

Trong bài báo này, mô hình bài toán tối ưu vector phụ thuộc tham số được tập trung nghiên cứu thông qua tập cải tiến và khảo sát tính liên tục Hausdorff của ánh xạ nghiệm hữu hiệu yếu cho các bài toán này. Trước tiên, một số tính chất của tập cải tiến được xây dựng. Sau đó, mô hình bài toán tối ưu vector thông qua tập cải tiến và nghiệm hữu hiệu yếu của chúng được đề xuất. Cuối cùng, bằng cách sử dụng các tính chất của tập cải tiến và tính lồi của hàm có giá trị vector, các điều kiện đủ cho tính liên tục Hausdorff của các ánh xạ nghiệm hữu hiệu yếu này được khảo sát.

Từ khóa: Bài toán tối ưu vector, nghiệm hữu hiệu yếu, tập cải tiến, tính liên tục Hausdorff

Article Details

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