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

Abstract

In this paper we propose a new large-update primal-dual interior point algorithm for P ∗( κ) 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 ∗( κ) 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 ∗( κ) LCPs have the polynomial complexity O q 3 2 ( 1 + 2 κ ) n ( log n ) q + 1 q log n ϵ which is better than the classical large-update primal-dual algorithm based on the classical logarithmic barrier function.