Communications of the Korean Mathematical Society (대한수학회논문집)

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

  • Cho, Gyeong-Mi (DEPARTMENT OF MULTIMEDIA ENGINEERING DONGSEO UNIVERSITY) ;
  • Kim, Min-Kyung (DEPARTMENT OF MATHEMATICS PUSAN NATIONAL UNIVERSITY)
  • Received : 2009.03.09
  • Published : 2010.10.31
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Abstract

In this paper we propose new primal-dual interior point methods (IPMs) for $P_*(\kappa)$ 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, $\psi(t)=\frac{t^2-1}{2}-{\int}^t_1e{^{q(\frac{1}{\xi}-1)}d{\xi}$, $q\;{\geq}\;1$. If a strictly feasible starting point is available and the parameter $q\;=\;\log\;\(1+a{\sqrt{\frac{2{\tau}+2{\sqrt{2n{\tau}}+{\theta}n}}{1-{\theta}}\)$, where $a\;=\;1\;+\;\frac{1}{\sqrt{1+2{\kappa}}}$, then new large-update primal-dual interior point algorithms have $O((1\;+\;2{\kappa})\sqrt{n}log\;n\;log\;{\frac{n}{\varepsilon}})$ iteration complexity which is the best known result for this method. For small-update methods, we have $O((1\;+\;2{\kappa})q{\sqrt{qn}}log\;{\frac{n}{\varepsilon}})$ iteration complexity.

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Acknowledgement

Supported by : National Research Foundation of Korea, Dongseo University

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