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Operations Research Transactions >

2016 , Vol. 20 >Issue 1: 118 - 124

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2016.01.012

Continuity of the solution set map to parametric weak vector equilibrium problems

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  • 1. School of Mathematics and Computational Science, Zunyi Normal College, Zunyi 563002, Guizhou, China; 2. School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, China

Received date: 2014-10-24

  Online published: 2016-03-15

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Abstract

In this paper, using the nonlinear scalarization method, we obtain the upper semicontinuity and lower semicontinuity of the solution mappings to parametric weak vector equilibrium problems. Some examples are given to illustrate our results.

Key words： parametric weak vector equilibrium problem; upper semicontinuity; lower semicontinuity; nonlinear scalarization

Cite this article

LUO Guowang, PENG Yanfang, LIU Yanmin, HUANG Jianwen . Continuity of the solution set map to parametric weak vector equilibrium problems[J]. Operations Research Transactions, 2016 , 20(1) : 118 -124 . DOI: 10.15960/j.cnki.issn.1007-6093.2016.01.012

References

[1] Li S J, Chen G Y, Teo K L. On the stability of generalized vector quasivariational inequality problems [J]. Journal of Optimization Theory and Applications, 2002, 113: 283-295.
[2] Huang N J, Li J, Thompson H B. Stability for parametric implicit vector equilibrium problems [J]. Decisions in Economics and Finance, 2006, 43: 1267-1274.
[3] Gong X H. Continuity of the solution set to parametric weak vector equilibrium problems [J]. Journal of Optimization Theory and Applications, 2008, 139: 35-46.
[4] Chen C R, Li S J, Teo K L. Solution semicontinuity of parametric generalized vector equilibrium problems [J]. Journal of Global Optimization, 2009, 45: 309-318.
[5] Li S J, Fang Z M. Lower semicontinuity of the solution mappings to a parametric generalized Ky Fan inequality [J]. Journal of Optimization Theory and Applications, 2010, 147: 507-515.
[6] Peng Z Y, Yang X M, Peng J W. On the lower semicontinuity of the solution mappings to parametric weak generalized Ky Fan inequality [J]. Journal of Optimization Theory and Applications, 2012, 152: 256-264.
[7] Wangkeeree R, Wangkeeree R, Rreechasilp P. Continuity of the solution mappings to parametric generalized vector equilibrium problems [J]. Applied Mathematics Letters, 2014, 29: 42-45.
[8] Chen G Y, Huang X X, Yang X Q. Vector Optimization: Set-Valued and Variational Analysis [M]. Berlin: Springer, 2005.
[9] Chen G Y, Goh C J, Yang X Q. Vector network equilibrium problems and nonlinear scalarization methods [J]. Mathematical Methods of Operations Research, 1999, 49: 239-253.
[10] Chen G Y, Yang X Q, Yu H. A nonlinear scalarization function and generalized quasi-vector equilibrium problems [J]. Journal of Global Optimization, 2005, 32: 451-466.
[11] Chen C R, Li M H. Holder continuity of solutions to parametric vector equilibrium problems with nonlinear scalarization [J]. Numerical Functional Analysis and Optimization, 2014, 35: 685-707.
[12] Aubin J P, Ekeland I. Applied Nonlinear Analysis [M]. New York: John Wiley Sons, 1984.
[13] Luc D T. Theory of vector optimization [M]//Lecture Notes in Economics and Mathematical Systems, New York: Spring-Verlag, 1989.
[14] Wang S H, Li Q Y. A projection iterative algorithm for strong vector equilibrium problem [J]. Optimization, 2014, DOI: 10.1080/02331934.2014.919501.
[15] Chen C R, Li S J. On the solution continuity of parametric generalized systems [J]. Pacific Journal of Optimization, 2010, 6: 141-151.
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