In a previous work the authors introduced a non{interior predictor-corrector path following algorithm for the monotone linear complementarity problem. The method uses Chen{Harker{Kanzow{Smale smoothing techniques to track the central path and employs a reened notion for the neighborhood of the central path to obtain the boundedness of the iterates under the assumption of monotonicity and the ex...

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...

We propose a new kind of inexact scheme for a family of generalized proximal point methods for the monotone complementarity problem. These methods, studied by Auslender, Teboulle and Ben-Tiba, converge under the sole assumption of existence of solutions. We prove convergence of our new scheme, as well as discuss its implementability.

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.

The tensor complementarity problem is a special instance in the class of nonlinear problems, which has many applications multi-person noncooperative games, hypergraph clustering problems and traffic equilibrium problems. Two most important research issues are how to identify solvability solve such via analyzing structure involved tensor. In this paper, based on concept monotone mappings, we int...

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...

Given M ∈ <n×n and q ∈ <, the linear complementarity problem (LCP) is to find (x, s) ∈ < × < such that (x, s) ≥ 0, s = Mx + q, x s = 0. By using the ChenHarker-Kanzow-Smale (CHKS) smoothing function, the LCP is reformulated as a system of parameterized smooth-nonsmooth equations. As a result, a smoothing Newton algorithm, which is a modified version of the Qi-Sun-Zhou algorithm [Mathematical Pr...