Existence of solutions to vector optimization problems via mixed-ordered cones
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Abstract
In this paper, a new cone is introduced and the convexity of strongly efficient solution sets to vector optimization problems via this cone is also discussed. Firstly, a mixed-ordered cone based on the positive Orthant cone, the Lorentz cone, and the Lexicographic cone is proposed. Then, the properties of the above cone and the relationships between it and others cones are observed. Finally, existence conditions and the convexity of the solution set to the vector optimization problem are formulated.
Tóm tắt
Trong bài báo này, một nón mới được giới thiệu và tính lồi của tập nghiệm hữu hiệu mạnh của một bài toán tối ưu vector thông qua nón mới này cũng được thảo luận. Đầu tiên, một nón thứ tự kết hợp dựa trên nón Orthant dương, nón Lorentz và nón từ điển được giới thiệu. Sau đó, các tính chất của nón này và mối quan hệ giữa nó với các nón khác được khảo sát. Cuối cùng, điều kiện tồn tại và tính lồi của tập nghiệm của bài toán tối ưu vector dựa trên nón mới được thiết lập.
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References
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