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On the solution of mathematical programming problems with equilibrium constraints

Summary: On the solution of mathematical programming
problems with equilibrium constraints
Roberto Andreani # Jos’e Mario Mart’nez +
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.


Source: Andreani, Roberto - Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas


Collections: Mathematics