NEW PRIMAL-DUAL INTERIOR POINT METHODS FOR P*(κ) LINEAR COMPLEMENTARITY PROBLEMS

Title & Authors
NEW PRIMAL-DUAL INTERIOR POINT METHODS FOR P*(κ) LINEAR COMPLEMENTARITY PROBLEMS
Cho, Gyeong-Mi; Kim, Min-Kyung;

Abstract
In this paper we propose new primal-dual interior point methods (IPMs) for $\small{P_*(\kappa)}$ linear complementarity problems (LCPs) and analyze the iteration complexity of the algorithm. New search directions and proximity measures are defined based on a class of kernel functions, $\small{\psi(t)=\frac{t^2-1}{2}-{\int}^t_1e{^{q(\frac{1}{\xi}-1)}d{\xi}}$, $\small{q\;{\geq}\;1}$. If a strictly feasible starting point is available and the parameter $\small{q\;=\;\log\;$$1+a{\sqrt{\frac{2{\tau}+2{\sqrt{2n{\tau}}+{\theta}n}}{1-{\theta}}$$}$, where $\small{a\;=\;1\;+\;\frac{1}{\sqrt{1+2{\kappa}}}}$, then new large-update primal-dual interior point algorithms have $\small{O((1\;+\;2{\kappa})\sqrt{n}log\;n\;log\;{\frac{n}{\varepsilon}})}$ iteration complexity which is the best known result for this method. For small-update methods, we have $\small{O((1\;+\;2{\kappa})q{\sqrt{qn}}log\;{\frac{n}{\varepsilon}})}$ iteration complexity.
Keywords
primal-dual interior point method;kernel function;complexity;polynomial algorithm;large-update;linear complementarity problem;
Language
English
Cited by
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