A new large-update interior point algorithm for P*(κ) LCPs based on kernel functions

Gyeong-Mi Cho

doi:10.1016/j.amc.2006.04.060

A new large-update interior point algorithm for P*(κ) LCPs based on kernel functions

2006-11-01

23

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AI

DOI：10.1016/j.amc.2006.04.060

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In this paper we propose a new large-update primal-dual interior point algorithm for P,,(K) linear complementarity problems (LCPs). Recently, Peng et al. introduced self-regular barrier functions for primal-dual interior point methods (IPMs) for linear optimization (LO) problems and reduced the gap between the practical behavior of the algorithm and its theoretical worst case complexity. We introduce a new class of kernel functions which is not logarithmic barrier nor self-regular in the complexity analysis of interior point method (IPM) for P-*(kappa) linear complementarity problem (LCP). New search directions and proximity measures are proposed based on the kernel function. We showed that if a strictly feasible starting point is available, then the new large-update primal-dual interior point algorithms for solving P.(K) LCPs have the polynomial complexity O(q(3/2)(1+ 2 kappa) root n(log n)(q+1/q) log n/epsilon) which is better than the classical large-update primal-dual algorithm based on the classical logarithmic barrier function. (c) 2006 Elsevier Inc. All rights reserved.

Keyword:

large-update interior point method

kernel function

complexity

polynomial algorithm

linear complementarity problem

A new large-update interior point algorithm for P*(κ) LCPs based on kernel functions

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