An infeasible interior-point algorithm with full-Newton steps for $$P_*(\kappa )$$ P ∗ ( κ ) horizontal linear complementarity problems based on a kernel function

Abstract

This paper contains an infeasible interior-point method for $$P_*(\kappa )$$ horizontal linear complementarity problem based on a kernel function. The kernel function is used to determine the search directions. These search directions differ from the usually used ones in some interior-point methods, and their analysis is more complicated. Main feature of our algorithm is that there is no calculation of the step size, i.e, we use full-Newton steps at each iteration. The algorithm constructs strictly feasible iterates for a sequence of perturbations of the given problem, close to its central path. Two types of full-Newton steps are used, feasibility steps and centering steps. The iteration bound matches the best-known iteration bound for these types of algorithms.