Large-update interior point algorithm for P∗-linear complementarity problem - Cho, Gyeong-Mi (Journal of inequalities and applications, 2014)
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 O ( ( 1 + 2 κ ) ( log p ) 3 n ( log n ) log n μ 0 ϵ ) 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.