Skip to main content
SpringerLink
Log in

Lower semicontinuity of the efficient solution mapping in semi-infinite vector optimization

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

This paper establishes some sufficient conditions for the lower semicontinuity of the efficient solution mapping for the semi-infinite vector optimization problem with perturbations of both the objective function and the constraint set in normed linear spaces. The constraint set is the set of weakly efficient solutions of vector equilibrium problem, and perturbed by the perturbation of the criterion mapping to the vector equilibrium problem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Naccache P H, Stability in multicriteria optimization, Journal of Mathematic Analysis and Applications, 1979, 68: 441–3.

    Article  MATH  MathSciNet  Google Scholar 

  2. Tanino T and Sawaragi Y, Stability of nondominated solutions in multicriteria decision-making, Journal of Optimization Theory and Applications, 1980, 30: 229–3.

    Article  MATH  MathSciNet  Google Scholar 

  3. Penot J P and Sterna-Karwat A, Parametrized multicriteria optimization: Continuity and closedness of optimal multifunctions, Journal of Mathematic Analysis and Applications, 1986, 120: 150–3.

    Article  MATH  MathSciNet  Google Scholar 

  4. Bednarczuk E M, Berge-Type theorems for vector optimization problems, Optimization, 1995, 32: 373–3.

    Article  MATH  MathSciNet  Google Scholar 

  5. Bednarczuk E M, A note on lower semicontinuity of minimal points, Nonlinear Analysis, 2002, 50: 285–3.

    Article  MATH  MathSciNet  Google Scholar 

  6. Chuong T D, Yao J C, and Yen N D, Further results on the lower semicontinuity of efficient point multifunctions, Pacific Journal of Optimization, 2010, 6: 405–3.

    MATH  MathSciNet  Google Scholar 

  7. Xiang S W and Zhou Y H, Continuity properties of solutions of vector optimization, Nonlinear Analysis, 2006, 64: 2496–3.

    Article  MATH  MathSciNet  Google Scholar 

  8. Todorov M I, Kuratowski convergence of the efficient sets in the parametric linear vector semiinfinite optimization, European Journal of Operational Research, 1996, 94: 610–3.

    Article  MATH  Google Scholar 

  9. Chuong T D, Huy N Q, and Yao J C, Pseudo-Lipschitz property of linear semi-infinite vector optimization problems, European Journal of Operational Research, 2010, 200: 639–3.

    Article  MATH  MathSciNet  Google Scholar 

  10. Chuong T D and Yao J C, Sufficient conditions for pseudo-Lipschitz property in convex semiinfinite vector optimization problems, Nonlinear Analysis, 2009, 71: 6312–3.

    Article  MATH  MathSciNet  Google Scholar 

  11. Chuong T D, Lower semicontinuity of the Pareto solution map in quasiconvex semi-infinite vector optimization, Journal of Mathematic Analysis and Applications, 2012, 388: 443–3.

    Article  MATH  MathSciNet  Google Scholar 

  12. Chuong T D, Huy N Q, and Yao J C, Stability of semi-infinite vector optimization problems under functional perturbations, Journal of Global Optimization, 2009, 45: 583–3.

    Article  MATH  MathSciNet  Google Scholar 

  13. Luc D T, Theory of Vector Optimization, Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, New York, 1989, 319.

    Google Scholar 

  14. Gong X H, Connectedness of the solution sets and scalarization for vector equilibrium problems, Journal of Optimization Theory and Applications, 2007, 133: 151–3.

    Article  MATH  MathSciNet  Google Scholar 

  15. Göpfert A, Riahi H, Tammer C, and Zǎlinescu C, Variational Methods in Partially Ordered Spaces, Springer-Verlag, New York, 2003.

    Google Scholar 

  16. Aubin J P and Ekeland I, Applied Nonlinear Analysis, New York, John Wiley & Son, 1984.

    MATH  Google Scholar 

  17. Fan K, A generalization of Tychonoff’s fixed point theorem, Mathematics Analysis, 1961, 142: 305–3.

    MATH  Google Scholar 

  18. Gong X H, Continuity of the solution set to parametric weak vector equilibrium problems, Journal of Optimization Theory and Applications, 2008, 139: 35–3.

    Article  MATH  MathSciNet  Google Scholar 

  19. Gong X H and Yao Y J, Lower semicontinuity of the set of efficient solutions for generalized systems, Journal of Optimization Theory and Applications, 2008, 138: 197–3.

    Article  MATH  MathSciNet  Google Scholar 

  20. Chen B and Gong X H, Continuity of the solution set to parametric set-valued weak vector equilibrium problems, Pacific Journal of Optimization, 2010, 6: 511–3.

    MATH  MathSciNet  Google Scholar 

  21. Li S J and Fang Z M, Lower semicontinuity of the solution mappings to a parametric generalized Ky Fan inequality, Journal of Optimization Theory and Applications, 2010, 147: 507–3.

    Article  MATH  MathSciNet  Google Scholar 

  22. Peng Z Y, Yang X M, and Peng J W, On the lower semicontinuity of the solution mappings to parametric weak generalized Ky Fan inequality, Journal of Optimization Theory and Applications, 2012, 152: 256–3.

    Article  MATH  MathSciNet  Google Scholar 

  23. Jahn J, Mathematical Vector Optimization in Partially-Ordered Linear Spaces, Germany: Peter Lang, Frankfurt an Main, 1986.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Nanchang University, Nanchang, 330031, China

    Xunhua Gong

Authors
  1. Xunhua Gong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xunhua Gong.

Additional information

This research is partially supported by the National Natural Science Foundation of China under Grant Nos. 11061023, 11201216, and 11471291.

This paper was recommended for publication by Editor WANG Shouyang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gong, X. Lower semicontinuity of the efficient solution mapping in semi-infinite vector optimization. J Syst Sci Complex 28, 1312–1325 (2015). https://doi.org/10.1007/s11424-015-3058-8

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-015-3058-8

Keywords

Search

Navigation