Tính liên thông của tập nghiệm hữu hiệu yếu cho bài toán tối ưu vector không lồi
Abstract
In this paper, the non-convex vector optimization problem was considered and discussed the properties of its weakly efficient solution set. Firstly, some concepts about generalized convexities of vector valued mappings were provided and studied their relationships. Next, based on the Hiriart-Urruty oriented distance function, a new nonlinear scalar function for the underlying problem was presented and investigated its pseudo semicontinuous property. Finally, these concepts and properties of the Hiriart-Urruty oriented distance function were used to formulate sufficient conditions for the existence and the connectedness of the weakly efficient solution set of the reference problem.
Tóm tắt
Trong bài báo này, bài toán tối ưu vector không lồi được xem xét và thảo luận các tính chất của tập nghiệm hữu hiệu yếu đối với bài toán này. Trước hết, một số khái niệm về tính lồi tổng quát của ánh xạ giá trị vector được đưa ra và nghiên cứu các mối quan hệ của chúng. Tiếp đó, dựa trên hàm khoảng cách định hướng theo nghĩa Hiriart-Urruty, một hàm vô hướng phi tuyến mới cho bài toán đang xét được giới thiệu và nghiên cứu tính giả nửa liên tục của nó. Cuối cùng, các khái niệm và tính chất của hàm khoảng cách định hướng Hiriart-Urruty được sử dụng để thiết lập các điều kiện đủ cho sự tồn tại và tính liên thông của tập nghiệm hữu hiệu yếu của bài toán trên.
Article Details
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