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.

This note focuses on a viscoelastodynamic problem being subject to unilateral boundary conditions. Under appropriate regularity assumptions on the initial data, the problem can be reduced to the pseudodifferential linear complementarity problem through Fourier analysis. We prove that this problem possesses a solution, which, is obtained as the limit of a sequence of solutions of penalized probl...

In this paper, we propose a Big-? smoothing method for solving the P 0 matrix linear complementarity problem. We study the trajectory deened by the augmented smoothing equations and global convergence of the method under an assumption that the original P 0 matrix linear complementarity problem has a solution. The method has been tested on the P 0 matrix linear complementarity problem with unbou...