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An Interior Point Algorithm for Mixed Complementarity Nonlinear Problems

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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.

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Acknowledgements

We thank the anonymous reviewer and A. Chapiro for help in improving the text. Angel E. R. Gutierrez was supported in part by FONDECYT “Generación Científica—Becas Nacionales—Fortalecimiento de Programas de doctorado en universidades peruanas” under Award 217-2014. José Herskovits was supported in part by CNPq and FAPERJ. Grigori Chapiro was supported in part by FAPEMIG under Award APQ-01377-15.

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Authors and Affiliations

  1. Instituto de Matemática y Ciencias Afines, Lima, Peru

    Angel E. R. Gutierrez

  2. Universidade Federal de Juiz de Fora, Juiz de Fora, Brazil

    Sandro R. Mazorche & Grigori Chapiro

  3. Military Institute of Engineering, Rio de Janeiro, Brazil

    José Herskovits

  4. COPPE, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil

    José Herskovits

Authors
  1. Angel E. R. Gutierrez
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  2. Sandro R. Mazorche
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  3. José Herskovits
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  4. Grigori Chapiro
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Correspondence to Grigori Chapiro.

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Communicated by Ole Sigmund.

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Gutierrez, A.E.R., Mazorche, S.R., Herskovits, J. et al. An Interior Point Algorithm for Mixed Complementarity Nonlinear Problems. J Optim Theory Appl 175, 432–449 (2017). https://doi.org/10.1007/s10957-017-1171-7

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  • DOI: https://doi.org/10.1007/s10957-017-1171-7

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