A New Searching Direction for Linear Complementarity Problems
In this paper, we investigate the properties of a simple function. As an application, we present a full-step interior-point algorithm for linear complementarity problem. The algorithm uses the simple function to determine the searching direction and define the neighborhood of central path. The full-step used in the algorithm has local quadratic convergence property according to the proximity function which is also constructed by this simple function. We derive the iteration complexity for the algorithm and obtain the best-known iteration bounds for linear complementarity problem.
Helen Zhang, Gang Shen and David Jin
L. P. Zhang and Y. H. Xu, "A New Searching Direction for Linear Complementarity Problems", Advanced Materials Research, Vols. 219-220, pp. 1089-1092, 2011