Skip to main content

Advertisement

SpringerLink
Log in

Mathematical Programming with System of Equilibrium Constraints

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

Abstract

In this paper, we study the mathematical program with system of equilibrium constraints. This problem contains bilevel program with system of equilibrium constraints, semi-infinite program with system of equilibrium constraints, mathematical program with Nash equilibrium constraints, mathematical program with system of mixed variational like inequalities constraints. We establish the existence theorems of mathematical program with system of equilibrium constraints under various assumptions.

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

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

    Google Scholar 

  • Bard J.F. (1998) Pratical Bilevel Optimization, Algorithms and Applications, Nonconvex Optimization and its Applications. Kluwer Academic Publishers, Dordrechlt

    Google Scholar 

  • Birbil S., Bouza G., Frenk J.B.G., Still G. (2006) Equilibrium constrained optimization problems. Eur. J. Operation Res. 169, 1108–1127

    Article  Google Scholar 

  • Fan K. (1961) A generalization of Tychonoff’s fixed point theorem. Math. Ann. 142, 305–310

    Article  Google Scholar 

  • Fan K. (1952) Fixed point and minimax theorems in locally convex topological linear spaces. Proc. Nat. Acad. Sci. U.S.A. 38, 121–126

    Article  Google Scholar 

  • Himmelberg C.J. (1972) Fixed point of compact multifunctions. J. Math. Anal. Appl. 38, 205–207

    Article  Google Scholar 

  • Lin L.J., Ansari Q.H. (2004) Collective fixed points and maximal elements with applications to abstract economies. J. Math. Anal. Appl. 296, 455–472

    Article  Google Scholar 

  • Lin L.J., Still G. (2006) Mathematical programs with equilibrium constraints: the existence of feasible points. Optimization 55(3): 205–219

    Article  Google Scholar 

  • Luo Z.Q., Pang J.S., Ralph D. (1997) Mathematical Program with Equilibrium Constraint. Cambridge University Press, Cambridge

    Google Scholar 

  • Stein O. (2003) Bilevel Strategies in Semi-infinite Programming. Kluwer Academy publishers, Dordrecht

    Google Scholar 

  • Stein O., Still G. (2002) On generalized semi-infinite optimization and bilevel optimization. Eur. J. Operation Res. 142(3): 442–462

    Article  Google Scholar 

  • Tan N.X. (1985) Quasi-variational inequalities in topological linear locally convex Hausdorff spaces. Math. Nachrichten 122, 231–245

    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.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lin, LJ. Mathematical Programming with System of Equilibrium Constraints. J Glob Optim 37, 275–286 (2007). https://doi.org/10.1007/s10898-006-9049-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10898-006-9049-5

Keywords

Search

Navigation