Adaptive full newton-step infeasible interior-point method for sufficient horizontal LCP

An adaptive full Newton-step infeasible-interior-point method for solving sufficient horizontal linear complementarity problems is analysed and sufficient conditions are given for the superlinear convergence of the sequence of iterates. The main feature of the method is that the parameter defining the Newton-step is adaptively chosen at each iteration, in contrast with previous full-Newton step methods where this parameter is kept fixed at all iterations. We mention that no superlinear convergence results are known for the latter methods. The theoretical complexity of our method matches the best known results in the literature. In the first algorithm, we assume that an upper bound for the handicap of the problem is known. The second algorithm does not depend on the handicap of the problem, so that it can readily be applied to any horizontal linear complementarity problem.