Document Type

Article

Publication Date

2011

Publication Title

SIAM Journal on Optimization

DOI

10.1137/090766735

ISSN

1095-7189

Abstract

We present an interior-point method for the P∗(κ)-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∗(κ)-LCPs based on the entire class of eligible kernel functions.

Comments

Copyright © by SIAM. Unauthorized reproduction of this article is prohibited. The Author may post the final published version of the Work on the Author's personal web site and on the web server of the Author's institution, provided that proper notice of the Publisher's copyright is included and that no separate or additional fees are collected for access to or distribution of the work. Article published in the SIAM Journal on Optimization.

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