Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities

A new quasi-Newton algorithm for the solution of general box constrained variational inequality problem (GVI(l, u, F, f)) is proposed in this paper. It is based on a reformulation of the variational inequality problem as a nonsmooth system of equations ...

A variational inequality problem with a mapping $g:\Re^n \to \Re^n$ and lower and upper bounds on variables can be reformulated as a system of nonsmooth equations $F(x)=0$ in $\Re^n$. Recently, several homotopy methods, such as interior point and ...

In this paper, we reformulate the variational inequality problem as an equivalent smooth non-linear equation system by introducing the Chen-Harker-Kanzow-Smale smoothing function. A new smoothing inexact Newton algorithm is proposed to solve the smooth ...