Unified Analysis of Kernel-Based Interior-Point Methods for $P_*(\kappa)$-Linear Complementarity Problems

Authors:
G. Lesaja;C. Roos
Affiliations:
goran@georgiasouthern.edu;c.roos@tudelft.nl
Venue:
SIAM Journal on Optimization
Year:
2010

Citing 12
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Abstract

We present an interior-point method for the $P_*(\kappa)$-linear complementarity problem (LCP) 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 and 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 long-step and short-step versions of the method for several specific eligible kernel functions. For some of them we match the best known iteration bounds for the long-step method, while for the short-step method the iteration bounds are of the same order of magnitude. As far as we know, this is the first paper that provides a unified approach and comprehensive treatment of interior-point methods for $P_*(\kappa)$-LCPs based on the entire class of eligible kernel functions. (The title of this article has been corrected.)