For the nonlinear complementarity problem we derive norm bounds for the error of an approximate solution, generalizing the known results for the linear case. Furthermore, we present a linear system with interval data, whose solution set contains the error of an approximate solution. We perform extensive numerical tests and compare the different approaches.

Recently, based upon the Chen-Harker-Kanzow-Smale smoothing function and the trajectory and the neighbourhood techniques, Hotta and Yoshise proposed a noninterior point algorithm for solving the nonlinear complementarity problem. Their algorithm is globally convergent under a relatively mild condition. In this paper, we modify their algorithm and combine it with the superlinear convergence theo...

Abstract In this paper, a new class of generalized nonlinear complementarity problems is introduced and studied, and an iterative algorithm, called the three-step iteration scheme with errors, is suggested. The existence and uniqueness of solution for the generalized nonlinear complementarity problem and the convergence, stability and weak stability of iterative sequence generated by the algori...

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.

A continuous function f with domain X and range f(X) in R n is weakly univalent if there is a sequence of continuous one-to-one functions on X converging to f uniformly on bounded subsets of X. In this article, we establish, under certain conditions, the connectedness of an inverse image f ?1 (q). The univalence results of Radulescu-Radulescu, Mor e-Rheinboldt, and Gale-Nikaido follow from our ...

The main purpose of this paper is to investigate some kinds of nonlinear complementarity problems (NCP). For the structured tensors, such as, symmetric positive definite tensors and copositive tensors, we derive the existence theorems on a solution of these kinds of nonlinear complementarity problems. We prove that a unique solution of the NCP exists under the condition of diagonalizable tensors.

In the solution methods of the symmetric cone complementarity problem (SCCP), the squared norm of a complementarity function serves naturally as a merit function for the problem itself or the equivalent system of equations reformulation. In this paper, we study the growth behavior of two classes of such merit functions, which are induced by the smooth EP complementarity functions and the smooth...

We propose a homogeneous model for the class of mixed horizontal linear complementarity problems. The proposed homogeneous model is always solvable and provides the solution of the original problem if it exists, or a certificate of infeasibility otherwise. Our formulation preserves the sparsity of the original formulation and does not reduce to the homogeneous model of the equivalent standard l...