The plain Newton-min algorithm to solve the linear complementarity problem (LCP for short) 0 ≤ x ⊥ (Mx + q) ≥ 0 can be viewed as a semismooth Newton algorithm without globalization technique to solve the system of piecewise linear equations min(x, Mx + q) = 0, which is equivalent to the LCP. When M is an M-matrix of order n, the algorithm is known to converge in at most n iterations. We show in...

In the present work, we determine intervals of convergence for the various parameters involved for what is known as the Generalized Accelerated Overrelaxation iterative method for the solution of the Linear Complementarity Problem. The convergence intervals found constitute sufficient conditions for the Generalized Accelerated Overrelaxation method to converge and are better than what have been...

In this paper, we establish a significant matrix class inclusion that seems to have been overlooked in the literature of the linear complementarity problem. We show that P∗, the class of sufficient matrices, is a subclass of L. In the course of demonstrating this inclusion, we introduce other new matrix classes that forge interesting new connections between known matrix classes.