A New Full-Newton Step O(n) Infeasible Interior-Point Algorithm for P_*(k)-horizontal Linear Complementarity Problems

摘要

In this paper, we first present a brief review about the feasible interior-point algorithm for P_*(k)-horizontal linear complementarity problems (HLCPs) based on new directions. Then we present a new infeasible interior-point algorithm for these problems. The algorithm uses two types of full-Newton steps which are called feasibility steps and centering steps. The algorithm starts from strictly feasible iterations of a perturbed problem, and feasibility steps find strictly feasible iterations for the next perturbed problem. By accomplishing a few centering steps for the new perturbed problem, we obtain strictly feasible iterations close enough to the central path of the new perturbed problem and prove that the same result on the order of iteration complexity can be obtained.