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.

bilevel programs, equilibrium problems, existence, generalized semi-infinite programming, genericity, mathematical programs with equilibrium constraints, problems with complementarity constraints
Existence and Stability Conditions of Equilibrium (jel C62), Business Administration and Business Economics; Marketing; Accounting (jel M), Production Management (jel M11), Transportation Systems (jel R4)
hdl.handle.net/1765/1068
ERIM Report Series Research in Management , Econometric Institute Research Papers
Report / Econometric Institute, Erasmus University Rotterdam
Erasmus Research Institute of Management

Birbil, S.I, Bouza, G, Frenk, J.B.G, & Still, G.J. (2003). Equilibrium Constrained Optimization Problems (No. ERS-2003-085-LIS). Report / Econometric Institute, Erasmus University Rotterdam. Retrieved from http://hdl.handle.net/1765/1068