关于半无限规划的对偶间隙

On Dual Gap of Semi-Infinite Programming

该文对半无限凸规划（P）提出了一个对偶问题（D1），证明（D1）与（P）无对偶间隙当且仅当Lagrange对偶问题（D）与（P）之间无对偶间隙，作者还利用方向导数给出一个新的刻划鞍点准则的方法．

This paper proposes a dual problem (D1) for a semi-infinite convex programming problem (P). It is proved that a sufficient and necessary condition of no dual gap between (D1) and (P) is no dual gap between (P) and Lagrange's dual problem(D) of (P).The saddle point criterion of (P) is a characterized by using the directional derivative.