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Quadratic Convergence of a Long-Step Interior-Point Method for Nonlinear Monotone Variational Inequality Problems

Author

Listed:
  • J. Sun

    (National University of Singapore)

  • G. Y. Zhao

    (National University of Singapore)

Abstract

This paper offers an analysis on a standard long-step primal-dual interior-point method for nonlinear monotone variational inequality problems. The method has polynomial-time complexity and its q-order of convergence is two. The results are proved under mild assumptions. In particular, new conditions on the invariance of the rank and range space of certain matrices are employed, rather than restrictive assumptions like nondegeneracy.

Suggested Citation

  • J. Sun & G. Y. Zhao, 1998. "Quadratic Convergence of a Long-Step Interior-Point Method for Nonlinear Monotone Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 97(2), pages 471-491, May.
    • Handle: RePEc:spr:joptap:v:97:y:1998:i:2:d:10.1023_a:1022691020204
    DOI: 10.1023/A:1022691020204
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    References listed on IDEAS

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    1. Stephen Wright & Daniel Ralph, 1996. "A Superlinear Infeasible-Interior-Point Algorithm for Monotone Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 21(4), pages 815-838, November.
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    Cited by:

    1. Y. B. Zhao & J. Y. Han, 1999. "Two Interior-Point Methods for Nonlinear P *(τ)-Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 102(3), pages 659-679, September.

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