A Class of Path-Following Interior-Point Methods for P_(∗)(κ)-Horizontal Linear Complementarity Problems

In this paper,a class of polynomial interior-point algorithms for P_(∗)(κ)-horizontal linear complementarity problems based on a newparametric kernel function is presented.The new parametric kernel function is used both for determining the search directions and for measuring the distance between the given iterate and theμ-center of the problem.We derive the complexity analysis for the algorithm,both with large and small updates.