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.

bilevel programs, equilibrium probems, existence of feasible points, 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)
dx.doi.org/10.1016/j.ejor.2004.07.075, hdl.handle.net/1765/19277
ERIM Top-Core Articles , Econometric Institute Reprint Series
European Journal of Operational Research
Erasmus Research Institute of Management

Birbil, S.I, Bouza, G, Frenk, J.B.G, & Still, G.J. (2006). Equilibrium constrained optimization problems. In European Journal of Operational Research (Vol. 169, pp. 1108–1127). doi:10.1016/j.ejor.2004.07.075