Equilibrium Constrained Optimization Problems
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)|
|ERIM Report Series Research in Management , Econometric Institute Research Papers|
|Report / Econometric Institute, Erasmus University Rotterdam|
|Organisation||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