多目标优化问题鲁棒有效解与真有效解之间的关系  

Relations Between Robust Efficient Solutions and Properly Efficient Solutions to Multiobjective Optimization Problems

作　　者：杨铭 李林廷 高英 YANG Ming;LI Linting;GAO Ying(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,P.R.China)

机构地区：[1]重庆师范大学数学科学学院

出　　处：《应用数学和力学》2019年第12期1364-1372,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11771064)~~

摘　　要：在一定条件下研究了多目标优化问题鲁棒有效解与真有效解之间的关系及鲁棒有效解的最优性条件.首先,给出多目标优化问题鲁棒弱有效解的概念,研究它与鲁棒有效解和真有效解之间的关系,举例说明了相关结果的合理性.其次,在次类凸和伪凸性假设下研究了鲁棒有效解的必要性条件和充分性条件.The relations between the robust efficient solutions and properly efficient solutions to multiobjective optimization problems were studied,and the optimality conditions for the robust efficient solutions were discussed.Firstly,the concept of weakly robust efficient solutions to multiobjective optimization problems was given.Then,the relations between the(weakly)robust efficient solutions and the properly efficient solutions were made clear.Several examples were given to illustrate the main results.Finally,the necessary and sufficient optimality conditions for the robust efficient solutions were established under the subconvexity and pseudoconvexity assumptions.

关 键 词：多目标优化问题 鲁棒有效解 真有效解 最优性条件 

分 类 号：O221[理学—运筹学与控制论]