关于Farkas引理证明的一点注记

许多关于非线性规划的专著,如1]、2]、3]等,在证明Farkas引理时都蕴含地用到:“有限生成的凸锥(finitely generated convex cone)为闭集”这样一个事实,但都忽略了对此作出证明。本文旨在于非线性规划的内容范围内证明这一重要事实,从而对上述专著中Farkas引理的证明作出补充。

A Note on the Proof of Farkas' Lemma

In works on nonlinear programming,e.g.1],2],3],etc.,Farkas'Lemma is usually proved by implicitly referring to the fact that a finitely generated convex cone is a closed set.But the proof of this point,which is not obvious,is always ignored. The present paper aims at proving this important fact within the contex of nonlinear programming to complete the proof of Farkas'Lemma.