关于凸分析问题的两个注记

Two notes of convex analysis problem

指出凸分析问题的两个定理(凹规划定理和对偶定理)的证明中所存在的漏洞,并给出正确的证明.首先,将凸集的端子集的概念推广到一般集合的端集,再利用推广后的端集正确地证明了凹规划定理.其次,给出局部凸空间的一个引理,并利用这个引理证明了共轭函数的对偶定理.

The paper point out that there are some mistakes in the proof of two theorems, which are the concave programming theorem and the conjugate theorem, of convex analysis problem. Firstly, we will be the concept of terminal subset of convex set generalized to the endset of general set. Then, we use it to prove the concave programming theorem. At last, we give a lemma in locally convex space and use it to prove the conjugate theorem of conjugate function.