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Operations Research Transactions >

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

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

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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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

Cite this article

TANG Liping, YANG Xinmin . A class of nonlinear scalarization theorem of vector optimization problems[J]. Operations Research Transactions, 2016 , 20(3) : 85 -91 . DOI: 10.15960/j.cnki.issn.1007-6093.2016.03.009

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