Smooth Newton Method Based on a New NCP Function for Solving Variational Inequality Problems

A Hybrid Newton Method for Solving Box Constrained Variational Inequality Problems via the D-gap Function

A box constrained variational inequality problem can be reformulated as an unconstrained minimization problem through the D-gap function. A hybrid Newton-type method is proposed for minimizing the D-gap function. Under suitable conditions, the algorithm is shown to be globally convergent and locally quadratically convergent. Some numerical results are also presented.

Solving the Cahn-Hilliard variational inequality with a semi-smooth Newton method

A hybrid Newton method for solving the variational inequality problem via the D-gap function

The variational inequality problem (VIP) can be reformulated as an unconstrained minimization problem through the D-gap function. It is proved that the D-gap function has bounded level sets for the strongly monotone VIP. A hybrid Newton-type method is proposed for minimizing the D-gap function. Under some conditions, it is shown that the algorithm is globally convergent and locally quadraticall...

A Hybrid Josephy-newton Method for Solving Box Constrained Variational Inequality Problems via the D-gap Function

A box constrained variational inequality problem can be reformulated as an unconstrained minimization problem through the D-gap function. Some basic properties of the aane variational inequality subproblems in the classical Josephy-Newton method are studied. A hybrid Josephy-Newton method is then proposed for minimizing the D-gap function. Under suitable conditions, the algorithm is shown to be...

A New Unconstrained Differentiable Merit Function for Box Constrained Variational Inequality Problems and a Damped Gauss-Newton Method

In this paper we propose a new unconstrained diierentiable merit function f for box constrained variational inequality problems VIP(l; u; F). We study various desirable properties of this new merit function f and propose a Gauss-Newton method in which each step only requires the solution of a system of linear equations. Global and superlinear convergence results for VIP(l; u; F) are obtained. K...