A First Order Predictor-corrector Infeasible Interior Point Method for Sufficient Linear Complementarity Problems in a Wide and Symmetric Neighborhood of the Central Path

In this paper, a new predictor-corrector method is proposed for solving sufficient linear complementarity problems (LCP) with an infeasible starting point. The method generates a sequence of iterates in a wide and symmetric neighborhood of the infeasible central path of the LCP. If the starting point is feasible or close to being feasible, then an ε-approximate solution is obtained in at most O((1 + κ)nL) iterations. For a large infeasible starting point, the iteration complexity is O((1+κ)2n3/2L). The algorithm also converges Q-quadratically to zero for nondegenerate problems. We also present a variant of the original algorithm which does not depend on κ.