不确定多目标优化的鲁棒解及强弱Kuhn-Tucker条件  

Robust Solutions and the Weak and Strong Kuhn-Tucker Conditions in Uncertain Multi-Objective Optimization

作　　者：李艳艳 赵洁 林安 LI Yanyan;ZHAO Jie;LIN An(School of Mathematics and Computer,Chongqing Normal University Foreign Trade College,Hechuan Chongqing 401520,China)

机构地区：[1]重庆师范大学涉外商贸学院数学与计算机学院,重庆401520

出　　处：《重庆师范大学学报（自然科学版）》2020年第1期130-134,共5页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.11671062);重庆师范大学涉外商贸学院校级科研项目(No.KY2018014);重庆市教委科学技术研究项目(No.KJ1500303);重庆市基础与前沿研究计划项目(No.cstc2015jcyjA00027)。

摘　　要：【目的】对不确定多目标优化问题的鲁棒解及相关性质进行讨论。【方法】基于Burachik定义的两个正则条件,提出两个新的正则条件,即鲁棒性正则条件,进而利用新正则条件对不确定多目标优化问题的鲁棒解进行研究。【结果】建立了该问题鲁棒有效解的弱Kuhn-Tucker必要条件和真鲁棒有效解的强Kuhn-Tucker必要条件。【结论】所得的主要结果是对最近一些研究工作的改进和推广。[Purposes]To discuss the robust solutions and related properties of uncertain multi-objective optimization problems.[Methods]Based on the two regular conditions defined by Burachik,two new regularity conditions are proposed,namely robust regularity conditions.Furthermore,under the condition of the new regularity,the robust solutions of uncertain multi-objective optimization problems with inequality constraints are studied.[Findings]The weak Kuhn-Tucker necessary condition of robust efficient solutions and strong Kuhn-Tucker necessary condition of Geoffrion properly robust efficient solutions are established.[Conclusions]The main results improve and generalize some recent research works.

关 键 词：不确定多目标优化 鲁棒性正则条件 鲁棒有效解 真鲁棒有效解 强弱Kuhn-Tucker条件 

分 类 号：O221.6[理学—运筹学与控制论]