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运筹学学报 >

2016 , Vol. 20 >Issue 3: 85 - 91

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2016.03.009

运筹学

向量优化问题的一类非线性标量化定理

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  • 1. 重庆工商大学数学与统计学院, 重庆 400067； 2. 重庆师范大学数学科学学院, 重庆 400047

收稿日期: 2015-01-14

  网络出版日期: 2016-09-15

基金资助

国家自然科学基金(Nos. 11431004, 11271391), 重庆市科委项目(Nos. cstc2016jcyjA0178, cstc2015jcyjB00001, cstc2014pt-sy00001), 重庆市教委项目(No. KJ1600613), 重庆工商大学校级项目(No. 670101574)

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A class of nonlinear scalarization theorem of vector optimization problems

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  • 1. College of Mathematics and Statistics, Chongqing Technology and Business University,  Chongqing 400067, China; 2. College of Mathematics Sciences, Chongqing Normal University, Chongqing 400047, China

Received date: 2015-01-14

  Online published: 2016-09-15

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摘要

利用Gertewitz泛函研究向量优化问题的一类非线性标量化问题. 证明了向量优化问题的(C, \varepsilon)-弱有效解或(C, \varepsilon)-有效解与标量化问题的近似解或严格近似解间的等价关系, 并估计了标量化问题的近似解．

关键词： 向量优化; 非线性标量化; Gertewitz泛函; (C; \varepsilon)-有效解; (C; \varepsilon)-弱有效解

本文引用格式

唐莉萍, 杨新民 . 向量优化问题的一类非线性标量化定理[J]. 运筹学学报, 2016 , 20(3) : 85 -91 . DOI: 10.15960/j.cnki.issn.1007-6093.2016.03.009

Abstract

In this paper, a class of nonlinear scalarization for vector optimization problem is investigated via Gertewitz functional. We mainly prove the fact that (C, \varepsilon)-weakly efficient solutions or (C, \varepsilon)-efficient solutions of vector optimization problem are equivalent to approximate solutions or strictly approximate solutions of scalar problem, and also  estimate the approximate solutions of this scalar problem.

Key words： vector optimization; nonlinear scalarization; Gertewitz functional; (C, \varepsilon)-efficient solution; (C, \varepsilon)-weakly efficient solution

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