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http://dx.doi.org/10.7858/eamj.2010.26.1.009

A LARGE-UPDATE INTERIOR POINT ALGORITHM FOR $P_*(\kappa)$ LCP BASED ON A NEW KERNEL FUNCTION  

Cho, You-Young (DEPARTMENT OF MATHEMATICS PUSAN NATIONAL UNIVERSITY)
Cho, Gyeong-Mi (DEPARTMENT OF MULTIMEDIA ENGINEERING DONGSEO UNIVERSITY)
Publication Information
East Asian mathematical journal / v.26, no.1, 2010 , pp. 9-23 More about this Journal
Abstract
In this paper we generalize large-update primal-dual interior point methods for linear optimization problems in [2] to the $P_*(\kappa)$ linear complementarity problems based on a new kernel function which includes the kernel function in [2] as a special case. The kernel function is neither self-regular nor eligible. Furthermore, we improve the complexity result in [2] from $O(\sqrt[]{n}(\log\;n)^2\;\log\;\frac{n{\mu}o}{\epsilon})$ to $O\sqrt[]{n}(\log\;n)\log(\log\;n)\log\;\frac{m{\mu}o}{\epsilon}$.
Keywords
primal-dual interior point method; kernel function; complexity; polynomial algorithm; linear optimization problem;
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