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Complementarity Active-Set Algorithm for Mathematical Programming Problems with Equilibrium Constraints

Author

Listed:
  • J. J. Júdice

    (Universidade de Coimbra
    Instituto de Telecomunicações)

  • H. D. Sherali

    (Virginia Polytechnic Institute
    Virginia State University)

  • I. M. Ribeiro

    (Universidade do Porto)

  • A. M. Faustino

    (Universidade do Porto)

Abstract

In this paper, an algorithm for solving a mathematical programming problem with complementarity (or equilibrium) constraints (MPEC) is introduced, which uses the active-set methodology while maintaining the complementarity restrictions throughout the procedure. Finite convergence of the algorithm to a strongly stationary point of the MPEC is established under reasonable hypotheses. The algorithm can be easily implemented by adopting any active-set code for nonlinear programming. Computational experience is included to highlight the efficacy of the proposed method in practice.

Suggested Citation

  • J. J. Júdice & H. D. Sherali & I. M. Ribeiro & A. M. Faustino, 2007. "Complementarity Active-Set Algorithm for Mathematical Programming Problems with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 134(3), pages 467-481, September.
    • Handle: RePEc:spr:joptap:v:134:y:2007:i:3:d:10.1007_s10957-007-9231-z
    DOI: 10.1007/s10957-007-9231-z
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    References listed on IDEAS

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    1. Holger Scheel & Stefan Scholtes, 2000. "Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity," Mathematics of Operations Research, INFORMS, vol. 25(1), pages 1-22, February.
    2. Joaquim Júdice & Ana Faustino & Isabel Ribeiro, 2002. "On the solution of NP-hard linear complementarity problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(1), pages 125-145, June.
    3. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
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    Cited by:

    1. Joaquim Júdice, 2012. "Algorithms for linear programming with linear complementarity constraints," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(1), pages 4-25, April.
    2. Andreani, R. & Júdice, J.J. & Martínez, J.M. & Martini, T., 2016. "Feasibility problems with complementarity constraints," European Journal of Operational Research, Elsevier, vol. 249(1), pages 41-54.

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