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...

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...

Extending our previous work Monteiro and Pang (1996), this paper studies properties of two fundamental mappings associated with the family of interior-point methods for solving monotone nonlinear complementarity problems over the cone of symmetric positive semideenite matrices. The rst of these maps lead to a family of new continuous trajectories which include the central trajectory as a specia...

Abstract: Our purpose of this paper is to solve a class of stochastic linear complementarity problems (SLCP) with finitely many elements. Based on a new stochastic linear complementarity problem function, a new semi-smooth least squares reformulation of the stochastic linear complementarity problem is introduced. For solving the semi-smooth least squares reformulation, we propose a feasible non...

An extension of the linear complementarity problem (LCP) of mathematical programming is the so-called rational complementarity problem (RCP). This problem occurs if complementarity conditions are imposed on input and output variables of linear dynamical input/state/output systems. The resulting dynamical systems are called linear complementarity systems. Since the RCP is crucial both in issues ...

A new algorithm for the solution of large-scale nonlinear complementarity problems is introduced. The algorithm is based on a nonsmooth equation reformulation of the complementarity problem and on an inexact Levenberg-Marquardt-type algorithm for its solution. Under mild assumptions, and requiring only the approximate solution of a linear system at each iteration, the algorithm is shown to be b...