不确定多目标优化鲁棒真有效解的最优性与对偶  

Optimality and Duality of Properly Robust Efficient Solutions in Uncertain Multi-Objective Optimization Problems

作　　者：畅泽芳 余国林[1] CHANG Zefang;YU Guolin(Institute of Applied Mathematics,North Minzu University,Yinchuan 750021,China)

机构地区：[1]北方民族大学应用数学研究所,宁夏银川750021

出　　处：《应用数学》2020年第2期507-515,共9页Mathematica Applicata

基　　金：国家自然科学基金资助(11861002);宁夏自然科学基金资助(NZ17112);北方民族大学重大专项(ZDZX201804);北方民族大学研究生创新项目(YCX19121);北方民族大学非线性分析与金融优化创新团队资助。

摘　　要：本文研究一类不确定性多目标优化问题鲁棒真有效解的最优性条件和对偶理论.首先,借助鲁棒真有效解的标量化定理,在鲁棒型闭凸锥约束品性下,建立了不确定多目标优化问题真有效解的最优性条件;其次,针对原不确定多目优化的Wolfe型对偶问题,得到关于鲁棒真有效解的强、弱对偶定理.This paper is devoted to the study of optimality conditions and duality theorems for properly robust efficient solutions to an uncertain multi-objective optimization problem.Firstly,by using of the scalarization theorem of properly robust efficient solutions,we present the optimality conditions under the assumption of closed convex cone constraint qualification.Secondly,for the Wolfe type dual problem to the primal uncertain multi-objective optimization,the strong and weak duality theorems are proposed for properly efficiency.

关 键 词：鲁棒多目标优化 真有效解 最优性条件 对偶 

分 类 号：O221.2[理学—运筹学与控制论] O224[理学—数学]