Skip to main content
SpringerLink
Log in

The Characterization of Efficiency and Saddle Point Criteria for Multiobjective Optimization Problem with Vanishing Constraints

  • Published:
Acta Mathematica Scientia Aims and scope Submit manuscript

Abstract

In this article, we focus to study about modified objective function approach for multiobjective optimization problem with vanishing constraints. An equivalent η-approximated multiobjective optimization problem is constructed by a modification of the objective function in the original considered optimization problem. Furthermore, we discuss saddle point criteria for the aforesaid problem. Moreover, we present some examples to verify the established results.

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. Achtziger W, Kanzow C. Mathematical programs with vanishing constraints: optimality conditions and constraint qualifications. Math Prog, 2008, 114(1): 69–99

    Article  MathSciNet  MATH  Google Scholar 

  2. Antczak T. A new approach to multiobjective programming with a modified objective function. J Global Optim, 2003, 27(4): 485–495

    Article  MathSciNet  MATH  Google Scholar 

  3. Antczak T. An η-approximation method in nonlinear vector optimization. Nonlinear Anal, 2005, 63(2): 225–236

    Article  MathSciNet  MATH  Google Scholar 

  4. Facchinei F, Pang J S. Finite-Dimensional Variational Inequalities and Complementarity Problems. New York: Springer, 2003

    MATH  Google Scholar 

  5. Hanson M A. On sufficiency of the Kuhn-Tucker conditions. J Math Anal Appl, 1981, 80(2): 545–550

    Article  MathSciNet  MATH  Google Scholar 

  6. Hoheisel T, Kanzow C. First and second-order optimality conditions for mathematical programs with vanishing constraints. Appl Math, 2007, 52(6): 495–514

    Article  MathSciNet  MATH  Google Scholar 

  7. Hoheisel T, Kanzow C. Stationary conditions for mathematical programs with vanishing constraints using weak constraint qualifications. J Math Anal Appl, 2008, 337(1): 292–310

    Article  MathSciNet  MATH  Google Scholar 

  8. Hoheisel T, Kanzow C. On the Abadie and Guignard constraint qualification for mathematical programmes with vanishing constraints. Optimization, 2009, 58(4): 431–448

    Article  MathSciNet  MATH  Google Scholar 

  9. Luo Z Q, Pang J S, Ralph D. Mathematical Programs with Equilibrium Constraints. Cambridge: Cambridge University Press, 1996

    Book  MATH  Google Scholar 

  10. Mishra S K, Singh V, Laha V, Mohapatra R N. On Constraint qualifications for multiobjective optimization problems with vanishing constraints//Optimization Methods, Theory and Applications. Berlin, Heidelberg: Springer, 2015: 95–135

    Google Scholar 

  11. Outrarata J V, Kocvara M, Zowe J. Nonsmooth Approach to Optimization Problems with Equilibrium Constraints. Dordrecht: Kluwer Academic Publishers, 1998

    Book  Google Scholar 

  12. Pareto V. Cours de Economie Politique. Switzerland: Rouge, Lausanne, 1896

    Google Scholar 

  13. Tanino T, Sawaragi Y. Duality theory in multiobjective programming. J Optim Theory Appl, 1979, 27(4): 509–529

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad, 826 004, Jharkhand, India

    Anurag Jayswal & Vivek Singh

Authors
  1. Anurag Jayswal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vivek Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vivek Singh.

Additional information

The research of the first author was financially supported by the CSIR, New Delhi, India through Grant no.: 25(0266)/17/EMR-II.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jayswal, A., Singh, V. The Characterization of Efficiency and Saddle Point Criteria for Multiobjective Optimization Problem with Vanishing Constraints. Acta Math Sci 39, 382–394 (2019). https://doi.org/10.1007/s10473-019-0204-8

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10473-019-0204-8

Key words

2010 MR Subject Classification

Search

Navigation