多目标优化问题(ε,ε)-拟近似解的非线性标量化  

NONLINEAR SCALARIZATIONS FOR(ε,ε)-APPROXIMATE QUASI SOLUTIONS OF MULTIOBJECTIVE OPTIMIZATION PROBLEMS

作　　者：岳瑞雪[1] 高英[1] 

机构地区：[1]重庆师范大学数学学院,重庆401331

出　　处：《数学杂志》2016年第3期615-626,共12页Journal of Mathematics

基　　金：国家自然科学基金(11201511);重庆市重点实验室专项项目(CSTC;2011KLORSE03);重庆市科委项目(cstc2015jcyjA00005);重庆市教委项目(KJ1500309)

摘　　要：本文研究了多目标优化问题的(ε,ε-)-拟近似解.利用文献[1]给出的多目标优化问题统一的非线性标量化问题,在没有任何凸性条件下,研究了多目标优化问题(ε,ε-)-拟近似解的充分和必要条件.最后,利用文献[2]中给出的的范数,对多目标优化问题的(ε,ε-)-拟近似解进行了非线性标量化刻画.本文第3节推广了文献[1]中的结果.In this paper,we consider（ε,ε-）-approximate quasi efficient solutions of multiobjective optimization problems.Based on the uniform nonlinear scalarization problems given in[1],we derive several necessary and sufficient conditions for（ε,ε^-）-approximate quasi efficient solutions of multiobjective optimization problems without any convexity conditions.Finally,using the norm given in the,we derive a kind of nonlinear scalarization problem for（ε,ε^-）-approximate quasi efficient solutions of multiobjective optimization problems.Section 3 in this paper extends the results in[1].

关 键 词：多目标优化 拟近似解 标量化 

分 类 号：O221.6[理学—运筹学与控制论]