Remarks on the generalized Newton method

Abstract

We give some convergence results for the generalized Newton method for the computation of zeros of nondifferentiable functions which we proposed in an earlier work. Our results show that the generalized method can converge quadratically when used to compute the zeros of the sum of a differentiable function and the (multivalued) subgradient of a lower semicontinuous proper convex function. The method is therefore effective for variational inequalities and can be used to find the minimum of a function which is the sum of a twice-differentiable convex function and a lower semicontinuous proper convex function. A numerical example is given.