Skip to main content
SpringerLink
Log in

On Gap Functions for Quasi-Equilibrium Problems Via Duality

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

We extend gap functions to quasi-equilibrium problems by using the duality results. In particular, we obtain new results for quasi-equilibrium problems known earlier for equilibrium problems and mixed quasi-variational inequalities.

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. E. Blum and W. Oettli, “From optimization and variational inequalities to equilibrium problems,” Math Stud. 63, No. 1-4, 123-145 (1994).

    MathSciNet  Google Scholar 

  2. D. Aussel and J. Cotrina, “An existence result for quasi-equilibrium problems,” J. Convex Anal. 24, No. 1, 55-66 (2017).

    MathSciNet  Google Scholar 

  3. J. Cotrina and J. Zúñiga, “A note on quasi-equilibrium problems,” textitOper. Res. Lett. 46, No. 1, 138-140 (2018).

    MathSciNet  Google Scholar 

  4. G. Bigi and M. Passacantando, “Gap functions for quasi-equilibria,” J. Glob. Optim. 66, No. 4, 791-810 (2016).

    Article  MathSciNet  Google Scholar 

  5. P. J. S. Santos, P. S. M. Santos, and S. Scheimberg, “A Newton-type method for quasiequilibrium problems and applications,” Optimization 71, No. 1, 7-32 (2022).

    Article  MathSciNet  Google Scholar 

  6. L. Altangerel, “Gap functions for quasi-variational inequalities via duality,” J. Inequal. Appl. Paper No. 13 (2018).

  7. M. Fukushima, “A class of gap functions for quasi-variational inequality problems,” J. Ind. Manag. Optim. 3, No. 2, 165-171 (2007).

    Article  MathSciNet  Google Scholar 

  8. K. Taji, “On gap functions for quasi-variational inequalities,” Abstr. Appl. Anal. 2008, Article ID 631361 (2008).

  9. R. I. Bot¸ and E. R. Csetnek, “Conjugate duality and the control of linear discrete systems,” J. Optim. Theory Appl. 159, No. 3, 576-589 (2013).

  10. L. Altangerel, R. I. Bot¸, and G. Wanka, “On gap functions for equilibrium problems via Fenchel duality,” Pac. J. Optim. 2, No. 3, 667-678 (2006).

  11. L. Altangerel, R. I. Bot¸, and G.Wanka, “On the construction of gap functions for variational inequalities via conjugate duality,” Asia-Pac. J. Oper. Res. 24, No. 3, 353-371 (2007).

  12. L. F. Bueno, G. Haeser, F. Lara, and F. N. Rojas, “An augmented Lagrangian method for quasi-equilibrium problems,” Comput. Optim. Appl. 76, No. 3, 737-766 (2020).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. German-Mongolian Institute for Resources and Technology Nalaikh district, Ulaanbaatar, 12800, Mongolia

    Lkhamsuren Altangere

Authors
  1. Lkhamsuren Altangere
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lkhamsuren Altangere.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Altangere, L. On Gap Functions for Quasi-Equilibrium Problems Via Duality. J Math Sci 279, 730–737 (2024). https://doi.org/10.1007/s10958-024-07055-7

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-024-07055-7

Search

Navigation