Sự tồn tại nghiệm của bài toán tối ưu vector thông qua tập co-radiant
Abstract
This paper considers vector optimization problems via co-radiant sets and studies the existence conditions of the Benson weakly efficient solutions of these problems. Firstly, the properties of radiant sets and co-radiant sets were discussed. Then, models of vector optimization problems via co-radiant sets and their Benson weakly efficient solutions were proposed. Finally, using the linear scalarization method, sufficient conditions for these Benson weakly efficient solutions are formulated.
Tóm tắt
Mô hình bài toán tối ưu vector thông qua tập co-radiant được xem xét và nghiên cứu các điều kiện tồn tại của nghiệm hữu hiệu yếu Benson cho các bài toán này. Trước tiên, các tính chất của tập radiant và tập co-radiant được thảo luận. Sau đó, mô hình bài toán tối ưu vector thông qua tập co-radiant và nghiệm hữu hiệu yếu Benson của chúng được đề xuất. Cuối cùng, bằng cách sử dụng phương pháp vô hướng hóa tuyến tính, các điều kiện đủ cho sự tồn tại của các nghiệm hữu hiệu yếu Benson này được thiết lập.
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