Jacobi iterative method for a class of variational inequality problem

Abstract

In previous studies, Jacobi iterative method had been already applied to a variational inequality problem(VIP) in which the given mapping f is differentiable, strictly diagonally isotone and off-diagonally isotone on R$^n$. It had been known that if this iteration converges, then it converges pretty fast. But its convergence was not guaranteed. In this thesis, we extend the above method to a VIP with upper bounds on the variables. And a perturbation technique has been devised to guarantee the convergence of the algorithm under certain assumptions.