多目标优化问题近似解的非线性标量化刻画  

NONLINEAR SCALARIZATIONS OF APPROXIMATE SOLUTIONS FOR MULTIOBJECTIVE PROGRAMMING PROBLEMS

作　　者：李小燕 李美术 高英 LI Xiao-yan;LI Mei-shu;GAO Ying(School of Mathematical Sciences,Chonqing Normal University,Chongqing 301331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《数学杂志》2018年第3期563-570,共8页Journal of Mathematics

基　　金：国家自然科学基金(11201511;11771064);重庆市科委项目(cstc2015jcyjA00005);重庆市教委项目(KJ1500309)

摘　　要：本文主要研究非线性标量化问题近似解与多目标优化问题近似解的关系.利用两种范数建立非线性标量化问题,得到了多目标优化问题近似有效解和近似真有效解的非线性标量化结果,并给出例子对主要结果进行了说明.In this paper, we study the relationships between approximate solutions of scalar problems and approximate solutions of multiobjective programming. By utilizing two kind of norms to establish scalar problems, the nonlinear scalarizations of approximate efficient solutions and approximate properly efficient solutions for multiobjective programming problems are obtained. Moreover, some examples are given to explain the main results.

关 键 词：多目标优化 近似解 范数 非线性标量化 

分 类 号：O221.6[理学—运筹学与控制论]