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An Interior Point Algorithm for Mixed Complementarity Nonlinear Problems

Author

Listed:
  • Angel E. R. Gutierrez

    (Instituto de Matemática y Ciencias Afines)

  • Sandro R. Mazorche

    (Universidade Federal de Juiz de Fora)

  • José Herskovits

    (Military Institute of Engineering
    Federal University of Rio de Janeiro)

  • Grigori Chapiro

    (Universidade Federal de Juiz de Fora)

Abstract

Nonlinear complementarity and mixed complementarity problems arise in mathematical models describing several applications in Engineering, Economics and different branches of physics. Previously, robust and efficient feasible directions interior point algorithm was presented for nonlinear complementarity problems. In this paper, it is extended to mixed nonlinear complementarity problems. At each iteration, the algorithm finds a feasible direction with respect to the region defined by the inequality conditions, which is also monotonic descent direction for the potential function. Then, an approximate line search along this direction is performed in order to define the next iteration. Global and asymptotic convergence for the algorithm is investigated. The proposed algorithm is tested on several benchmark problems. The results are in good agreement with the asymptotic analysis. Finally, the algorithm is applied to the elastic–plastic torsion problem encountered in the field of Solid Mechanics.

Suggested Citation

  • Angel E. R. Gutierrez & Sandro R. Mazorche & José Herskovits & Grigori Chapiro, 2017. "An Interior Point Algorithm for Mixed Complementarity Nonlinear Problems," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 432-449, November.
    • Handle: RePEc:spr:joptap:v:175:y:2017:i:2:d:10.1007_s10957-017-1171-7
    DOI: 10.1007/s10957-017-1171-7
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    References listed on IDEAS

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    1. Grigori Chapiro & Angel E. R. Gutierrez & José Herskovits & Sandro R. Mazorche & Weslley S. Pereira, 2016. "Numerical Solution of a Class of Moving Boundary Problems with a Nonlinear Complementarity Approach," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 534-550, February.
    2. J. Herskovits, 1998. "Feasible Direction Interior-Point Technique for Nonlinear Optimization," Journal of Optimization Theory and Applications, Springer, vol. 99(1), pages 121-146, October.
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    Cited by:

    1. Chuangyin Dang & P. Jean-Jacques Herings & Peixuan Li, 2022. "An Interior-Point Differentiable Path-Following Method to Compute Stationary Equilibria in Stochastic Games," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1403-1418, May.
    2. 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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