Tính nửa liên tục dưới của nghiệm bài toán cân bằng vector và áp dụng vào bài toán tối ưu vector
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Abstract
The paper considers the parametric vector equilibrium problem in the Hausdorff topological vector spaces. By utilizing properties of a scalarizing function constructed based on the Hiriart-Urruty oriented distance function along with appropriate conditions and techniques, sufficient conditions for the lower semicontinuity of the solution maps of the problems under consideration are established. This achieved result is novel and is applicable to vector optimization problems.
Tóm tắt
Bài báo xem xét bài toán cân bằng vector phụ thuộc tham số trong không gian vector tô pô Hausdorff. Bằng việc sử dụng các tính chất của hàm vô hướng hoá được xây dựng dựa vào hàm khoảng cách định hướng Hiriart-Urruty cùng với các điều kiện cũng như kỹ thuật thích hợp khác, các điều kiện đủ cho tính nửa liên tục dưới của ánh xạ nghiệm hữu hiệu bài toán đang xét đã được thiết lập. Kết quả đạt được này là mới và được áp dụng cho bài toán tối ưu vector.
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