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It is well known that each barrier function defines an interior point algorithm and each barrier function is determined by its univariate kernel function. In this paper we present a new large-update primal-dual interior point algorithm for solving P * -linear complementarity problem (LCP) based on a parametric version of the kernel function in (Bai et al. in SIAM J. Optim. 13:766-782, 2003). We show that the algorithm has) iteration complexity, where p is a barrier function parameter and κ is the handicap of the matrix. This is the best known complexity result for such a method. MSC: 90C33; 90C51

In this paper we propose a new large-update primal-dual interior point algorithm for P * ( ) linear complementarity problems (LCPs). We generalize Bai et al.'s [A primal-dual interior-point method for linear optimization based on a new proximity function, Optim. Methods Software 17(2002) 985-1008] primal-dual interior point algorithm for linear optimization (LO) problem to P * ( ) LCPs. New search directions and proximity measures are proposed based on a kernel function which is not logarithmic barrier nor self-regular for P * ( ) LCPs. We showed that if a strictly feasible starting point is available, then the new large-update primaldual interior point algorithm for solving P * ( ) LCPs has the polynomial complexity O((1 + 2 )n 3/4 log(n/ )) and gives a simple complexity analysis. This proximity function has not been used in the complexity analysis of interior point method (IPM) for P * ( ) LCPs before.