概率约束线性规划最优解的存在性

The EXistence of the Optimal Solution for the Probabilistic Constrained Linear Programming Problem

本文给出了概率约束规划ｍｉｎ的最优值有限的充要条件；对一类离散型随机向量ξ，并给出了这一概率约束规划存在最优解的充要条件．实际中常用的离散型随机向量属于这类离散型随机向量．

We discuss the problem(P)min,where A_1,A_2 are non-random matrices and b,c are non-random vectors,p(0<p<1) is a constant reliabilitylevel,ξis a discrete random vector.Necessary and sufficient conditions of the optimalvalue of(P)being finite are presented.For one kind of practical discrete random vectors,the necessary and sufficient conditions for existence of an optimal solution of(P)are given.