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On the convergence rate of Newton interior-point methods in the absence of strict complementarity

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Abstract

In the absence of strict complementarity, Monteiro and Wright [7] proved that the convergence rate for a class of Newton interior-point methods for linear complementarity problems is at best linear. They also established an upper bound of 1/4 for the Q 1-factor of the duality gap sequence when the steplengths converge to one. In the current paper, we prove that the Q 1 factor of the duality gap sequence is exactly 1/4. In addition, the convergence of the Tapia indicators is also discussed.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt

    A. S. El-Bakry

  2. the Center for Research on Parallel Computations, Rice University, 77521-1892, Houston, Texas, USA

    A. S. El-Bakry

  3. Department of Computational and Applied Mathematics, Rice University, 77521-1892, Houston, Texas, USA

    R. A. Tapia

  4. the Center for Research on Parallel Computations, Rice University, 77521-1892, Houston, Texas, USA

    R. A. Tapia

  5. Department of Mathematics and Statistics, University of Maryland, Baltimore County, 21228, Baltimore, MD, USA

    Y. Zhang

Authors
  1. A. S. El-Bakry
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  2. R. A. Tapia
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  3. Y. Zhang
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Additional information

This author was supported in part by NSF Coop. Agr. No. CCR-8809615 and AFOSR 89-0363 and the REDI Foundation.

This author was supported in part by NSF Coop. Agr. No. CCR-8809615, AFOSR 89-0363, DOE DEFG05-86ER25017 and ARO 9DAAL03-90-G-0093.

Visiting member of the Center for Research on Parallel Computations, Rice University, Houston, Texas, 77251-1892. This author was supported in part by DOE DE-FG02-93ER25171.

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El-Bakry, A.S., Tapia, R.A. & Zhang, Y. On the convergence rate of Newton interior-point methods in the absence of strict complementarity. Comput Optim Applic 6, 157–167 (1996). https://doi.org/10.1007/BF00249644

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  • DOI: https://doi.org/10.1007/BF00249644

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