Quy tắc Fermat cho các đa chức năng trên không gian Banach

Springer Science and Business Media LLC - Tập 104 - Trang 69-90 - 2005
Xi Yin Zheng1, Kung Fu Ng2
1Department of Mathematics, Yunnan University, Kunming, P.R. China
2Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong

Tóm tắt

Sử dụng phân tích biến phân, chúng tôi nghiên cứu các bài toán tối ưu véc tơ với các mục tiêu là các đa chức năng đóng trên các không gian Banach hoặc trong các không gian Asplund. Cụ thể, dựa trên các đạo hàm đồng nhất, chúng tôi trình bày quy tắc Fermat như là các điều kiện cần để tìm nghiệm tối ưu cho các bài toán trên. Như là các ứng dụng, chúng tôi cũng cung cấp một số điều kiện cần (dựa trên các nón bình thường của Clarke hoặc các nón bình thường giới hạn) cho các điểm Pareto hiệu quả.

Từ khóa


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