多目标决策的逼近方法（Ⅰ）：理论分析  

APPROXIMATION METHOD FOR MULTIOBJECTIVE DECISION MAKING(Ⅰ):THEORETICAL ANALYSIS

作　　者：施保昌[1,2] 陈王廷[1,2] 胡新生[1,2] 周济 

机构地区：[1]华中理工大学系统工程研究所 [2]华中理工大学CAD中心

出　　处：《系统工程学报》1996年第3期1-10,共10页Journal of Systems Engineering

摘　　要：本文将函数序列的ｖ－收敛性（ｖａｒｉａｔｉｏｎａｌｃｏｎｖｅｒｇｅｎｃｅ）推广到向量值函数，在ｖ－收敛性的条件下得到了给定的多目标决策问题的近似弱有效解集的下半连续性并给出了若干容易验证的充分条件．在一致收敛性和不变凸性（ｉｎｖｅｘｉｔｙ）的条件下得到了近似有效解集的连续性．作为本文一般性结果的应用，得到了求解多目标ｍｉｎｉｍａｘ（最小最大）问题的一种有效的逼近方法：极大熵方法的收敛性质．The variational convergence of real function sequence is extended to vector function sequence and the lower semicontinuity of approximating set of weak Pareto solutions of a given multiobjective decision making problem with general constraint set is obtained by using the variational convergence. By using the uniform convergence and invexity the continuity of the approximating set of Pareto solutions of the problem is obtained. Then as the applications of the general results, the convergent properties of a kind of efficient approximating method: maximum entropy method for multiobjective minimax problems are obtained.

关 键 词：多目标决策 逼近法 决策 非线性规划 

分 类 号：O225[理学—运筹学与控制论]