A new large-update interior point algorithm for linear complementarity problems

In this paper we propose a new large-update primal-dual interior point algorithm for P * ( κ ) linear complementarity problems (LCPs). We generalize Bai et al.ʹs [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 ) 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 ) 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 ) LCPs has the polynomial complexity O ( ( 1 + 2 κ ) n 3 / 4 log ( 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 ) LCPs before.