Primal-Dual Affine Scaling Interior Point Methods for Linear Complementarity Problems

A first order affine scaling method and two mth order affine scaling methods for solving monotone linear complementarity problems (LCP) are presented. All three methods produce iterates in a wide neighborhood of the central path. The first order method has O(nL2(lognL2)(log lognL2)) iteration complexity. If the LCP admits a strict complementary solution then both the duality gap and the iteration sequence converge superlinearly with Q-order two. If m = Ω(log( √ nL)), then both higher order methods have O( √ n)L iteration complexity. The Q-order of convergence of one of the methods is (m + 1) for problems that admit a strict complementarity solution while the Q-order of convergence of the other method is (m + 1)/2 for general monotone LCPs.