Equilibrium Constrained Optimization Problems

25 Pages Posted: 26 Aug 2006

See all articles by S. Ilker Birbil

S. Ilker Birbil

C. N. Bouza

University of Havana - Department of Applied Mathematics

J. B. G. Frenk

Erasmus University, Rotterdam (EUR) - Department of Econometrics ; Erasmus University, Rotterdam (EUR) - Erasmus Research Institute of Management (ERIM)

G. Still

University of Twente - Department of Applied Mathematics

Date Written: December 3, 2003

Abstract

We consider equilibrium constrained optimization problems, which have a general formulationthat encompasses well-known models such as mathematical programs with equilibrium constraints, bilevel programs, and generalized semi-infinite programming problems. Based on the celebrated K K M lemma, we prove the existence of feasible points for the equilibrium constraints. Moreover, we analyze the topological and analytical structure of the feasible set. Alternative formulations of an equilibrium constrained optimization problem (ECOP) that are suitable for numerical purposes are also given. As an important _rst step for developing ef_cient algorithms, we provide a genericity analysis for the feasible set of a particular ECOP, for which all the functions are assumed to be linear.

Keywords: bilevel programs, equilibrium problems, existence, generalized semi-infinite programming, mathematical programs with equilibrium constraints, problems with complementarity constraints, genericity

JEL Classification: R4, M, M11, C62

Suggested Citation

Birbil, S. Ilker and Bouza, Carlos N. and Frenk, J.B.G. (Hans) and Still, G., Equilibrium Constrained Optimization Problems (December 3, 2003). ERIM Report Series Reference No. ERS-2003-085-LIS. Available at SSRN: https://ssrn.com/abstract=483852

Carlos N. Bouza

University of Havana - Department of Applied Mathematics ( email )

Havana
Cuba

J.B.G. (Hans) Frenk

Erasmus University, Rotterdam (EUR) - Department of Econometrics ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands
+31 0 10 408 1257 (Phone)
+31 0 10 408 9162 (Fax)

Erasmus University, Rotterdam (EUR) - Erasmus Research Institute of Management (ERIM)

P.O. Box 1738
3000 DR Rotterdam
Netherlands

G. Still

University of Twente - Department of Applied Mathematics ( email )

P.O. Box 217
7500 AE Enschede
Netherlands
+31 53 489 3404 (Phone)
+31 53 489 4858 (Fax)

HOME PAGE: http://wwwhome.math.utwente.nl/~stillgj/

No contact information is available for S. Ilker Birbil

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