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Kernel-Based Interior-Point Methods for Monotone Linear Complementarity Problems over Symmetric Cones

Author

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  • G. Lesaja

    (Georgia Southern University)

  • C. Roos

    (Delft University of Technology)

Abstract

We present an interior-point method for monotone linear complementarity problems over symmetric cones (SCLCP) that is based on barrier functions which are defined by a large class of univariate functions, called eligible kernel functions. This class is fairly general and includes the classical logarithmic function, the self-regular functions, as well as many non-self-regular functions as special cases. We provide a unified analysis of the method and give a general scheme on how to calculate the iteration bounds for the entire class. We also calculate the iteration bounds of both large-step and short-step versions of the method for ten frequently used eligible kernel functions. For some of them we match the best known iteration bound for large-step methods, while for short-step methods the best iteration bound is matched for all cases. The paper generalizes results of Lesaja and Roos (SIAM J. Optim. 20(6):3014–3039, 2010) from P ∗(κ)-LCP over the non-negative orthant to monotone LCPs over symmetric cones.

Suggested Citation

  • G. Lesaja & C. Roos, 2011. "Kernel-Based Interior-Point Methods for Monotone Linear Complementarity Problems over Symmetric Cones," Journal of Optimization Theory and Applications, Springer, vol. 150(3), pages 444-474, September.
    • Handle: RePEc:spr:joptap:v:150:y:2011:i:3:d:10.1007_s10957-011-9848-9
    DOI: 10.1007/s10957-011-9848-9
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    References listed on IDEAS

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    1. Y. Q. Bai & G. Lesaja & C. Roos & G. Q. Wang & M. El Ghami, 2008. "A Class of Large-Update and Small-Update Primal-Dual Interior-Point Algorithms for Linear Optimization," Journal of Optimization Theory and Applications, Springer, vol. 138(3), pages 341-359, September.
    2. Yu. E. Nesterov & M. J. Todd, 1997. "Self-Scaled Barriers and Interior-Point Methods for Convex Programming," Mathematics of Operations Research, INFORMS, vol. 22(1), pages 1-42, February.
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    Cited by:

    1. H. Saberi Najafi & S. A. Edalatpanah, 2013. "On the Convergence Regions of Generalized Accelerated Overrelaxation Method for Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 859-866, March.

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