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

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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.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA, 30460-8093, USA

    G. Lesaja

  2. Faculty of Electrical Engineering, Mathematics, and Computer Science, Delft University of Technology, P.O. Box 5031, 2600, GA Delft, The Netherlands

    C. Roos

Authors
  1. G. Lesaja
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  2. C. Roos
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Correspondence to G. Lesaja.

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Communicated by F.A. Potra.

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Lesaja, G., Roos, C. Kernel-Based Interior-Point Methods for Monotone Linear Complementarity Problems over Symmetric Cones. J Optim Theory Appl 150, 444–474 (2011). https://doi.org/10.1007/s10957-011-9848-9

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  • DOI: https://doi.org/10.1007/s10957-011-9848-9

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