A generalized direction in interior point method for monotone linear complementarity problems

In this paper, we present a new interior point method with full Newton step for monotone linear complementarity problems. The specificity of our method is to compute the Newton step using a modified system similar to that introduced by Darvay in Stud Univ Babe-Bolyai Ser Inform 47:15-26,2017. We prove that this new method possesses the best known upper bound complexity for these methods. Moreover, we extend results known in the literature since we consider a general family of smooth concave functions in the Newton system instead of the square root.