Tính đóng và tính nửa liên tục trên của nghiệm hữu hiệu bài toán cân bằng vector
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Abstract
This paper studies vector equilibrium problems in normed spaces. Firstly, the paper provides sufficient conditions for the closedness of efficient solution sets of reference problems. Subsequently, the paper studies the useful properties of a nonlinear scalarization function in the sense of generalized oriented Hiriart-Urruty introduced in the literature. These properties are utilized to establish sufficient conditions for the upper semicontinuity of efficient solution maps of the considered problems when the data are perturbed.
Tóm tắt
Bài báo nghiên cứu bài toán cân bằng vector trong không gian định chuẩn. Trước hết, bài báo đưa ra các điều kiện đủ cho tính đóng của tập nghiệm hữu hiệu của bài toán đang xét. Tiếp theo, bài báo khảo sát một số tính chất hữu dụng của một hàm vô hướng hoá phi tuyến dạng Hiriart-Urruty mở rộng đã được giới thiệu trong tài liệu. Các tính chất này được dùng để thiết lập các điều kiện đủ cho tính nửa liên tục trên của ánh xạ nghiệm hữu hiệu cho bài toán đang xét khi dữ liệu của bài toán bị nhiễu.
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