- 作者: 賴漢卿
- 作者服務機構: 國立清華大學數學研究所
- 中文摘要: 本文研究從一局部凸性實數拓樸線性空間映到Dedekind完備Riesz空間的凸算子之對偶最佳化問題。其目的在於原始問題的可行解與其對偶問題的可行解,用一攝動函數來連結,推導出一極值等式。這個等式表現出原始問題與其對偶問題之最佳解的關係。由此關係,古典的 Fenchel 對偶定理以及廣義的 Fenchel 對偶定理,都可在本文之結果中導出來。
- 英文摘要: This paper studies the dual optimization problems of convex operators from a locally convex realtopological vector space to a Dedekind complete Riesz space. The aim is to give an identity linked by apurturbed function between the feasible solutions of a primal problem and its dual problem. The classicalFenchel's duality theorem and the generalized Fenchel's duality theorem are then the consequence of theresult described in the context.
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