In this paper, we consider a new non-interior continuation method for the solution of nonlinear complementarity problem with $P_0$-function ($P_0$-NCP). The proposed algorithm is based on a smoothing symmetric perturbed minimum function (SSPM-function), and one only needs to solve one system of linear equations and to perform only one Armijo-type line search at each iteration. The method is proved to possess global and local convergence under weaker conditions. Preliminary numerical results indicate that...

We propose a penalty approach for a box constrained variational inequality problem $\left(\mathrm{BVIP}\right)$. This problem is replaced by a sequence of nonlinear equations containing a penalty term. We show that if the penalty parameter tends to infinity, the solution of this sequence converges to that of $\mathrm{BVIP}$ when the function $F$ involved is continuous and strongly monotone and the box $C$ contains the origin. We develop the algorithmic aspect with theoretical arguments properly established. The numerical results tested on...

Existence of a solution to the quasi-variational inequality problem arising in a model for sand surface evolution has been an open problem for a long time. Another long-standing open problem concerns determining the dual variable, the flux of sand pouring down the evolving sand surface, which is also of practical interest in a variety of applications of this model. Previously, these problems were solved for the special case in which the inequality is simply variational. Here, we introduce a regularized...

In this paper, we study the strong convergence of the proximal gradient algorithm with inertial extrapolation term for solving classical minimization problem and finding the fixed points of $\delta$-demimetric mapping in a real Hilbert space. Our algorithm is inspired by the inertial proximal point algorithm and the viscosity approximation method of Moudafi. A strong convergence result is achieved in our result without necessarily imposing the summation condition ${\sum }_{n=1}^{\infty }{\beta }_n\parallel x_{n-1}-x_n\parallel <+\infty$ on the inertial term. Finally, we provide...