Summary: On the solution of mathematical programming
problems with equilibrium constraints
Roberto Andreani # Jose Mario Martnez +
July 26, 2002
Mathematical programming problems with equilibrium constraints
(MPEC) are nonlinear programming problems where the constraints
have a form that is analogous to firstorder optimality conditions of
constrained optimization. We prove that, under reasonable su#cient
conditions, stationary points of the sum of squares of the constraints
are feasible points of the MPEC. In usual formulations of MPEC all the
feasible points are nonregular in the sense that they do not satisfy the
MangasarianFromovitz constraint qualification of nonlinear program
ming. Therefore, all the feasible points satisfy the classical FritzJohn
necessary optimality conditions. In principle, this can cause serious
di#culties for nonlinear programming algorithms applied to MPEC.
However, we show that most feasible points do not satisfy a recently
introduced stronger optimality condition for nonlinear programming.
This is the reason why, in general, nonlinear programming algorithms
are successful when applied to MPEC.