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On the solution of mathematical programming problems with equilibrium constraints

Author

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  • Roberto Andreani
  • José Mario Martı´nez

Abstract

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. Copyright Springer-Verlag Berlin Heidelberg 2001

Suggested Citation

  • Roberto Andreani & José Mario Martı´nez, 2001. "On the solution of mathematical programming problems with equilibrium constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 54(3), pages 345-358, December.
    • Handle: RePEc:spr:mathme:v:54:y:2001:i:3:p:345-358
    DOI: 10.1007/s001860100158
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    Cited by:

    1. J.M. Martínez & B.F. Svaiter, 2003. "A Practical Optimality Condition Without Constraint Qualifications for Nonlinear Programming," Journal of Optimization Theory and Applications, Springer, vol. 118(1), pages 117-133, July.
    2. A. Izmailov & M. Solodov, 2009. "Examples of dual behaviour of Newton-type methods on optimization problems with degenerate constraints," Computational Optimization and Applications, Springer, vol. 42(2), pages 231-264, March.
    3. R. Andreani & S. Castro & J. Chela & A. Friedlander & S. Santos, 2009. "An inexact-restoration method for nonlinear bilevel programming problems," Computational Optimization and Applications, Springer, vol. 43(3), pages 307-328, July.
    4. Feijoo, Felipe & Das, Tapas K., 2014. "Design of Pareto optimal CO2 cap-and-trade policies for deregulated electricity networks," Applied Energy, Elsevier, vol. 119(C), pages 371-383.

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