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Polynomiality of primal-dual affine scaling algorithms for nonlinear complementarity problems

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Abstract

This paper provides an analysis of the polynomiality of primal-dual interior point algorithms for nonlinear complementarity problems using a wide neighborhood. A condition for the smoothness of the mapping is used, which is related to Zhu’s scaled Lipschitz condition, but is also applicable to mappings that are not monotone. We show that a family of primal-dual affine scaling algorithms generates an approximate solution (given a precision ε) of the nonlinear complementarity problem in a finite number of iterations whose order is a polynomial ofn, ln(1/ε) and a condition number. If the mapping is linear then the results in this paper coincide with the ones in Jansen et al., SIAM Journal on Optimization 7 (1997) 126–140.

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Authors and Affiliations

  1. Faculty of Technical Mathematics and Informatics, Delft University of Technology, P.O. Box 5031, 2600 GA, Delft, The Netherlands

    Benjamin Jansen, Kees Roos & Tamás Terlaky

  2. Institute of Socio Economic Planning, University of Tsukuba, 305, Tsukuba, Ibaraki, Japan

    Akiko Yoshise

Authors
  1. Benjamin Jansen
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  2. Kees Roos
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  3. Tamás Terlaky
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  4. Akiko Yoshise
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Additional information

Research supported in part by Grant-in-Aids for Encouragement of Young Scientists (06750066) from the Ministry of Education, Science and Culture, Japan.

Research supported by Dutch Organization for Scientific Research (NWO), grant 611-304-028

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Jansen, B., Roos, K., Terlaky, T. et al. Polynomiality of primal-dual affine scaling algorithms for nonlinear complementarity problems. Mathematical Programming 78, 315–345 (1997). https://doi.org/10.1007/BF02614359

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  • DOI: https://doi.org/10.1007/BF02614359

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