向量优化问题的一类非线性标量化定理

doi:10.15960/j.cnki.issn.1007-6093.2016.03.009

Operations Research Transactions

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A class of nonlinear scalarization theorem of vector optimization problems

TANG Liping¹ YANG Xinmin^2,*

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:2015-01-14 Online:2016-09-15 Published:2016-09-15

Abstract

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

TANG Liping, YANG Xinmin. A class of nonlinear scalarization theorem of vector optimization problems[J]. Operations Research Transactions, doi: 10.15960/j.cnki.issn.1007-6093.2016.03.009.

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A class of nonlinear scalarization theorem of vector optimization problems

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