Predictor-corrector methods for sufficient linear complementarity problems in a wide neighborhood of the central path

Two predictor-corrector methods of order m = Ω(logn) are proposed for solving sufficient linear complementarity problems. The methods produce a sequence of iterates in the N− ∞ neighborhood of the central path. The first method requires an explicit upper bound κ of the handicap of the problem while the second method does not. Both methods have O((1 + κ)1+1/m √ nL) iteration complexity. They are superlinearly convergent of order m + 1 for nondegenerate problems and of order (m + 1)/2 for degenerate problems. The cost of implementing one iteration is at most O(n3) arithmetic operations.