Equilibrium Constrained Optimization Problems
25 Pages Posted: 26 Aug 2006
Date Written: December 3, 2003
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
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