An interior-point algorithm for horizontal linear complementarity problems

This paper presents a wide-neighbourhood interior-point algorithm for P-horizontal linear complementarity problem. The convergence analysis is shown for the introduced wide neighbourhood of the central path by Ai and Zhang (2005) for monotone linear complementarity problem, and unifies the analysis for its constituent wide neighbourhoods. The Newton search directions are decomposed to the non-negative and non-positive parts, correspond to the parts of the right hand side. The achieved complexity bound is the same as the best obtained bound for the monotone linear complementarity problems, except that it is multiplied by a factor dependent on the handicap of the given problem.