Equilibrium constrained optimization problems

Ş.İ. Birbil, G. Bouza Allende, J.B.G. Frenk, Georg J. Still

Research output: Contribution to journalArticleAcademicpeer-review

22 Citations (Scopus)

Abstract

We consider equilibrium constrained optimization problems, which have a general formulation that encompasses well-known models such as mathematical programs with equilibrium constraints, bilevel programs, and generalized semi-infinite programming problems. Based on the celebrated KKM 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 first step for developing efficient algorithms, we provide a genericity analysis for the feasible set of a particular ECOP, for which all the functions are assumed to be linear.
Original languageUndefined
Article number10.1016/j.ejor.2004.07.075
Pages (from-to)1108-1127
Number of pages20
JournalEuropean journal of operational research
Volume169
Issue numberWP06-03/3
DOIs
Publication statusPublished - 16 Mar 2006

Keywords

  • EWI-8136
  • IR-63681
  • METIS-237605

Cite this

Birbil, Ş. İ., Bouza Allende, G., Frenk, J. B. G., & Still, G. J. (2006). Equilibrium constrained optimization problems. European journal of operational research, 169(WP06-03/3), 1108-1127. [10.1016/j.ejor.2004.07.075]. https://doi.org/10.1016/j.ejor.2004.07.075