The nonlinear complementarity problem has been used to study and formulate various equilibrium problems including the traffic equilibrium problem, the spatial equilibrium problem and the Nash equilibrium problem. To solve the nonlinear complementarity problem, various iterative methods such as projection methods, linearized methods and Newton method have been proposed and their convergence resu...

This paper presents a non-interior point method for a frictionless contact problem in the large deformation, where we can exploit the warm start condition in an incremental path-following method such as the arc-length method. We propose a novel reformulation of the nonlinear complementarity problem based on the smoothed Fischer–Burmeister function, in which the smoothing parameter is considered...

We discuss local convergence of Newton’s method to a singular solution x∗ of the nonlinear equations F (x) = 0, for F : IR → IR. It is shown that an existing proof of Griewank, concerning linear convergence to a singular solution x∗ from a starlike domain around x∗ for F twice Lipschitz continuously differentiable and x∗ satisfying a particular regularity condition, can be adapted to the case i...

In this paper, we introduce and study a class of generalized nonlinear complementarity problems and construct an iterative algorithm, called the Noor iterations with errors, by using the change of variables technique. We establish the existence and uniqueness of solution of the generalized nonlinear complementarity problem and the convergence and stability of iterative sequence generated by the...

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 a recent paper by Chen and Mangasarian (C. Chen, O.L. Mangasarian, A class of smoothing functions for nonlinear and mixed complementarity problems, Computational Optimization and Applications 2 (1996), 97±138) a class of parametric smoothing functions has been proposed to approximate the plus function present in many optimization and complementarity related problems. This paper uses these sm...