We are interested in the solution of Horizontal Linear Complementarity Problems, HLCPs, that is complementarity problems with more variables than equations. Globally metrically regular HLCPs have nonempty solution sets that are stable with respect to “right-hand-side perturbations” of the data, hence are numerically attractive. The main purpose of the paper is to show how the stability or condi...

Three interior point methods are proposed for sufficient horizontal linear complementarity problems (HLCP): a large update path following algorithm, a first order corrector-predictor method, and a second order corrector-predictor method. All algorithms produce sequences of iterates in the wide neighborhood of the central path introduced by Ai and Zhang. The algorithms do not depend on the handi...

A new class of infeasible interior point methods for solving sufficient linear complementarity problems requiring one matrix factorization andm backsolves at each iteration is proposed and analyzed. The algorithms from this class use a large (N− ∞) neighborhood of an infeasible central path associated with the complementarity problem and an initial positive, but not necessarily feasible, starti...