Skip to main content
SpringerLink
Log in

Existence Results for Primal and Dual Generalized Vector Equilibrium Problems With Applications to Generalized Semi-Infinite Programming

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

Abstract

In this paper, we introduce several kinds of maximal pseudomonotonicity and establish existence theorems of maximal pseudomonotonicity. From these results we establish the existence theorems of generalized vector equilibrium problems. We establish existence theorems of generalized vector semi-infinite programming, as applications of generalized vector equilibrium problems.

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

  • Q.H. Ansari (2000) Vector equilibrium problems and vector variational inequalities F. Giannessi (Eds) Variational Inequalities and Vector Equilibria. Mathematical Theories Kluwer Academic Publishers Dordrecht 1–16

    Google Scholar 

  • Ansari Q.H., Konnov I.V., Yao J.C. (2001). On generalized vector equilibrium problems. Nonlinear Analysis: Theory, Methods and Applications, 543–554

  • Q.H. Ansari J.C. Yao (1999) ArticleTitleAn existence result for the generalized vector equilibrium problems Applied Mathematics and Letters, 53 IssueID-56 53–56

    Google Scholar 

  • J.P. Aubin A. Cellina (1994) Differential Inclusions Springer-Verlag Berlin, Germany

    Google Scholar 

  • M. Bianchi N. Hadjisavvas S. Schaible (1997) ArticleTitleVector equilibrium problems with generalized monotone bifunctions Journal of Optimization Theory and Applications. 92 527–542 Occurrence Handle10.1023/A:1022603406244

    Article  Google Scholar 

  • E. Blum W. Oettli (1994) ArticleTitleFrom optimization and variational inequalities to equilibrium problems The Mathematics Students. 63 123–146

    Google Scholar 

  • T.H. Chang C.L. Yen (1996) ArticleTitleKKM properties and fixed point theorems Journal of Mathematical Analysis Application. 203 224–235

    Google Scholar 

  • U. Faigle W. Kern G. Still (2003) Algorithmic Principles of Mathematical Programming Kluwer Academic Publishers Dordrecht, The Netherlands

    Google Scholar 

  • J.Y. Fu (2000) ArticleTitleGeneralized vector quasi-equilibrium problems Mathematical Methods of Operations Research. 52 57–64

    Google Scholar 

  • F. Giannessi (Eds) (2000) Variational Inequalities and Vector Equilibria. Mathematical Theories Kluwer Academic Publisher Dordrecht, Holland

    Google Scholar 

  • R. John (2001) A note on Minty variational inequalities and generalized Monotonicity N. Hadjisavvas J.E. Martinez-Legaz J.P. Penot (Eds) Generalized Convexity and Generalized Monotonicity. Springer-Verlag Berlin

    Google Scholar 

  • I.V. Konnov J.C. Yao (1997) ArticleTitleOn the generalized vector variational inequality problem Journal of Mathematical Analysis and Applications. 206 42–58 Occurrence Handle10.1006/jmaa.1997.5192

    Article  Google Scholar 

  • I.V. Konnov (1998) ArticleTitleOn quasimonotone variational inequalities Journal Optimization Theory and Applications. 99 165–181

    Google Scholar 

  • I.V. Konnov J.C. Yao (1999) ArticleTitleExistence solutions for generalized vector equilibrium problems Journal Mathematical Analysis and Applications. 223 328–335

    Google Scholar 

  • I.V. Konnov (2001) On vector equilibrium and vector variational inequality problems N. Hadjisavvas J.E. Martinez-Legaz J.P. Penot (Eds) Generalized Convexity and Generalized Monotonicity. Springer-Verlag Berlin

    Google Scholar 

  • M. Lassonde (1983) ArticleTitleOn the use of KKM multifunctions in fixed point theory and related topics Journal of Mathematical Analysis Applications. 97 151–201

    Google Scholar 

  • S. Komlosi (1999) On the Stampachia and Minty variational inequalities G. Giorgi F.A. Rossi (Eds) Generalized Convexity and Optimization for Economic and Financial Decision. Pitagora Editrice Bologna

    Google Scholar 

  • L.J. Lin Z.T. Yu (2001) ArticleTitleFixed point theorems and equilibrium problems Nonlinear Analysis Theory Methods and Applications. 43 987–999

    Google Scholar 

  • L.J. Lin Q.H. Ansari J.Y. Wu (2003) ArticleTitleGeometric properties and coincidence theorems with applications to generalized vector equilibrium problems Journal Optimization Theory and Applications. 117 121–137

    Google Scholar 

  • L.J. Lin Z.T. Yu G. Kassay (2002) ArticleTitleExistence of equilibria for monotone multivalued mappings and its applications to vectorial equilibria Journal of Optimization Theory and Applications. 114 189–208 Occurrence Handle10.1023/A:1015420322818

    Article  Google Scholar 

  • N.X. Tan (1985) ArticleTitleQuasi-variational inequalities in topological linear locally convex Hausdorff spaces Mathematical Nach. 122 231–245

    Google Scholar 

  • N.C. Yannelis N.D. Prabhaker (1983) ArticleTitleExistence of maximal elements and equilibria in linear topological spaces Journal of Mathematical Economics. 12 233–245 Occurrence Handle10.1016/0304-4068(83)90041-1

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, National Changhua University of Education, Changhua, 50058, Taiwan

    Lai-Jiu Lin

Authors
  1. Lai-Jiu Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lai-Jiu Lin.

Additional information

This research was supported by the National Science Council of the Republic of China.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lin, LJ. Existence Results for Primal and Dual Generalized Vector Equilibrium Problems With Applications to Generalized Semi-Infinite Programming. J Glob Optim 33, 579–595 (2005). https://doi.org/10.1007/s10898-004-6096-7

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10898-004-6096-7

Keywords

Search

Navigation