Mathematical Methods of Operations Research

, Volume 54, Issue 3, pp 345–358 | Cite as

On the solution of mathematical programming problems with equilibrium constraints

  • Roberto Andreani
  • José Mario Martı´nez


Mathematical programming problems with equilibrium constraints (MPEC) are nonlinear programming problems where the constraints have a form that is analogous to first-order optimality conditions of constrained optimization. We prove that, under reasonable sufficient 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 Mangasarian-Fromovitz constraint qualification of nonlinear programming. Therefore, all the feasible points satisfy the classical Fritz-John necessary optimality conditions. In principle, this can cause serious difficulties 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.

Key words: Mathematical programming with equilibrium constraints optimality conditions minimization algorithms reformulation 
AMS: 90C33 90C30 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Roberto Andreani
    • 1
  • José Mario Martı´nez
    • 2
  1. 1.Department of Computer Science and Statistics, University of the State of S. Paulo (UNESP), C.P. 136, CEP 15054-000, São José do Rio Preto-SP, Brazil. (E-mail:
  2. 2.Department of Applied Mathematics, IMECC-UNICAMP, University of Campinas, CP 6065, 13081-970 Campinas SP, Brazil. (E-mail:

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