Skip to main content
SpringerLink
Log in

Lexicographic and sequential equilibrium problems

  • Published:
Journal of Global Optimization Aims and scope Submit manuscript

Abstract

The aim of this work is to analyze lexicographic equilibrium problems on a topological Hausdorff vector space X, and their relationship with some other vector equilibrium problems. Existence results for the tangled lexicographic problem are proved via the study of a related sequential problem. This approach was already followed by the same authors in the case of 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.

Similar content being viewed by others

References

  1. Blum E., Oettli W.: From optimization and variational inequalities to equilibrium problem. Math. Stud. 63, 123–145 (1994)

    Google Scholar 

  2. Konnov I.V.: On lexicographic vector equilibrium problems. J. Optmi. Theory Appl. 118, 681–688 (2003)

    Article  Google Scholar 

  3. Bianchi M., Konnov I., Pini R.: Lexicographic variational inequalities with applications. Optimization 56, 355–367 (2007)

    Article  Google Scholar 

  4. Hadjisavvas, N., Khatibzadeh, H.: Maximal monotonicity of bifunctions. Optimization (forthcoming)

  5. Daniilidis A., Hadjisavvas N.: On the subdifferentials of quasiconvex and pseudoconvex functions and cyclic monotonicity. J. Math. Anal. Appl. 237, 30–42 (1999)

    Article  Google Scholar 

  6. Crouzeix J.-P., Marcotte P., Zhu D.: Conditions ensuring the applicability of cutting-plane methods for solving variational inequalities. Math. Program. 88, 521–539 (2000)

    Article  Google Scholar 

  7. Bianchi M., Kassay G., Pini R.: Existence of equilibria via Ekeland’s principle. J. Math. Anal. Appl. 305, 502–512 (2005)

    Article  Google Scholar 

  8. Lin L.-J., Du W.-S.: On maximal element theorems, variants of Ekeland’s variational principle and their applications. Nonlinear Anal. 68, 1246–1262 (2008)

    Article  Google Scholar 

  9. Djafari Rouhani B., Tarafdar E., Watson P.J.: Existence of solutions to some equilibrium problems. J. Optim. Appl. 126, 97–107 (2005)

    Article  Google Scholar 

  10. Konnov I.V., Ali M.S.S.: Descent methods for monotone equilibrium problems in Banach spaces. J. Comput. Appl. Math. 188, 165–179 (2006)

    Article  Google Scholar 

  11. Chadli O., Chbani Z., Riahi H.: Equilibrium problems with generalized monotone bifunctions and applications to variational inequalities. J. Optim. Theory Appl. 105, 299–323 (2000)

    Article  Google Scholar 

  12. Bianchi M., Pini R.: Coercivity conditions for equilibrium problems. J. Optim. Theory Appl. 120, 79–92 (2005)

    Article  Google Scholar 

  13. Konnov I.V.: Regularization method for nonmonotone equilibrium problems. J. Nonlinear Convex Anal. 10, 93–101 (2009)

    Google Scholar 

  14. Brézis H., Nirenberg L., Stampacchia G.: A remark on Ky Fan’s minimax principle. Bolletino della Unione Matematica Italiana 6, 293–300 (1972)

    Google Scholar 

  15. Bianchi M., Pini R.: A note on equilibrium problems with properly quasimonotone bifunctions. J. Global Optim. 20, 67–76 (2001)

    Article  Google Scholar 

  16. Avriel M., Diewert W.E., Schaible S., Zang I.: Generalized Concavity. Plenum Press, New York and London (1988)

    Google Scholar 

  17. Tversky A.: Intransitivity of preferences. Psychol. Rev. 76, 31–48 (1969)

    Article  Google Scholar 

  18. Shafer W.: The non-transitive consumer. Econometrica 42, 913–919 (1974)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Discipline Matematiche, Finanza Matematica ed Econometria, Università Cattolica, Largo Gemelli, 1, 20123, Milano, Italy

    M. Bianchi

  2. Department of System Analysis and Information Technologies, Kazan University, ul. Kremlevskaya, 18, 420008, Kazan, Russia

    I. V. Konnov

  3. Dipartimento di Metodi Quantitativi per le Scienze Economiche e Aziendali, Università Milano-Bicocca, Via Bicocca degli Arcimboldi, 8, 20126, Milano, Italy

    R. Pini

Authors
  1. M. Bianchi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. V. Konnov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. R. Pini
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. V. Konnov.

Additional information

In this work, the second author was supported in part by RFBR–NNSF Grant No. 07-01-92101.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bianchi, M., Konnov, I.V. & Pini, R. Lexicographic and sequential equilibrium problems. J Glob Optim 46, 551–560 (2010). https://doi.org/10.1007/s10898-009-9439-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10898-009-9439-6

Keywords

Search

Navigation