A new large-update interior point algorithm for P*(κ)P*(κ) linear complementarity problems

In this paper we propose a new large-update primal-dual interior point algorithm for P*(κ)P*(κ) 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*(κ)P*(κ) LCPs. New search directions and proximity measures are proposed based on a kernel function which is not logarithmic barrier nor self-regular for P*(κ)P*(κ) LCPs. We showed that if a strictly feasible starting point is available, then the new large-update primal-dual interior point algorithm for solving P*(κ)P*(κ) LCPs has the polynomial complexity O((1+2κ)n3/4log(n/ε))O((1+2κ)n3/4log(n/ε)) and gives a simple complexity analysis. This proximity function has not been used in the complexity analysis of interior point method (IPM) for P*(κ)P*(κ) LCPs before.