Skip to main content
SpringerLink
Log in

Lower Studniarski derivative of the perturbation map in parametrized vector optimization

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

In this paper, by virtue of lower Studniarski derivatives of set-valued maps, relationships between lower Studniarski derivative of a set-valued map and its profile map are discussed. Some results concerning sensitivity analysis are obtained in parametrized vector optimization.

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. Bonnans J.F., Shapiro A.: Perturbation Analysis of Optimization Problems. Springer, New York (2000)

    MATH  Google Scholar 

  2. Fiacco A.V.: Introduction to Sensitivity and Stablity Analysis in Nonlinear Programming. Academic Press, New York (1983)

    Google Scholar 

  3. Tanino T.: Sensitivity analysis in multiobjective optimization. J. Optim. Theory Appl. 56, 479–499 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  4. Shi D.S.: Contingent derivative of the perturbation map in multiobjective optimization. J. Optim. Theory Appl. 70, 385–396 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  5. Shi D.S.: Sensitivity analysis in convex vector optimization. J. Optim. Theory Appl. 77, 145–159 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  6. Kuk H., Tanino T., Tanaka M.: Sensitivity analysis in vector optimization. J. Optim. Theory Appl. 89, 713–730 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  7. Kuk H., Tanino T., Tanaka M.: Sensitivity analysis in parametrized convex vector optimization. J. Math. Anal. Appl. 202, 511–522 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  8. Giannessi F.: Theorems of the alternative, quadratic programs and complementarity problems. In: Cottle, R.W., Giannessi, F., Lions, J.L. (eds) Variational Inequalities and Complementarity Problems, pp. 151–186. Wiley, New York (1980)

    Google Scholar 

  9. Li S.J., Yan H., Chen G.Y.: Differential and sensitivity properties of gap functions for vector variational inequalities. Math. Methods Oper. Res. 57, 377–391 (2003)

    MathSciNet  MATH  Google Scholar 

  10. Meng K.W., Li S.J.: Differential and sensitivity properties of gap functions for Minty vector variational inequalities. J. Math. Anal. Appl. 337, 386–398 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  11. Li M.H., Li S.J.: Second order differential and sensitivity properties of weak vector variational inequalities. J. Optim. Theory Appl. 144, 76–87 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  12. Li, S.J., Sun, X.K.: Higher order optimality conditions for strict local minimality in set-valued optimization (under review)

  13. Aubin J.P., Frankowska H.: Set-Valued Analysis. Birkhauser, Boston (1990)

    MATH  Google Scholar 

  14. Sawaragi Y., Nakayama H., Tanino T.: Theory of Multiobjective Optimization. Academic Press, New York (1985)

    MATH  Google Scholar 

  15. Holmes R.B.: Geometric Functional Analysis and its Applications. Springer, New York (1975)

    MATH  Google Scholar 

  16. Luc D.T.: Theory of Vector Optimization. Springer, Berlin (1989)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Mathematics and Sciences, Chongqing University, Chongqing, 400030, China

    X. K. Sun & S. J. Li

Authors
  1. X. K. Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. J. Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to X. K. Sun.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sun, X.K., Li, S.J. Lower Studniarski derivative of the perturbation map in parametrized vector optimization. Optim Lett 5, 601–614 (2011). https://doi.org/10.1007/s11590-010-0223-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-010-0223-9

Keywords

Search

Navigation