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Smoothing Methods for Nonlinear Complementarity Problems

Author

Listed:
  • Mounir Haddou

    (INSA-IRMAR)

  • Patrick Maheux

    (Université d’Orléans)

Abstract

In this paper, we present some new smoothing techniques to solve general nonlinear complementarity problems. Under a weaker condition than monotonicity as on the original problems, we prove convergence of our methods. We also present an error estimate under a general monotonicity condition. Some numerical tests confirm the efficiency of the proposed methods.

Suggested Citation

  • Mounir Haddou & Patrick Maheux, 2014. "Smoothing Methods for Nonlinear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 711-729, March.
    • Handle: RePEc:spr:joptap:v:160:y:2014:i:3:d:10.1007_s10957-013-0398-1
    DOI: 10.1007/s10957-013-0398-1
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    References listed on IDEAS

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    1. A. Auslender & R. Cominetti & M. Haddou, 1997. "Asymptotic Analysis for Penalty and Barrier Methods in Convex and Linear Programming," Mathematics of Operations Research, INFORMS, vol. 22(1), pages 43-62, February.
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    Cited by:

    1. L. Abdallah & M. Haddou & T. Migot, 2019. "A sub-additive DC approach to the complementarity problem," Computational Optimization and Applications, Springer, vol. 73(2), pages 509-534, June.
    2. Giandomenico Mastroeni & Letizia Pellegrini & Alberto Peretti, 2021. "Some numerical aspects on a method for solving linear problems with complementarity constraints," Working Papers 16/2021, University of Verona, Department of Economics.
    3. Vu, Duc Thach Son & Ben Gharbia, Ibtihel & Haddou, Mounir & Tran, Quang Huy, 2021. "A new approach for solving nonlinear algebraic systems with complementarity conditions. Application to compositional multiphase equilibrium problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 1243-1274.
    4. Yiyin Cao & Chuangyin Dang & Yabin Sun, 2022. "Complementarity Enhanced Nash’s Mappings and Differentiable Homotopy Methods to Select Perfect Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 192(2), pages 533-563, February.

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