On the Convergence of Newton-like Method for Variational Inclusions under Pseudo-Lipschitz Mapping

Abstract

In the present paper, we study a Newton-like method for solving the variational inclusion defined by the sums of a Frechet differentiable function, divided difference admissible function and a set-valued mapping with closed graph. Under some suitable assumptions on the Frechet derivative of the differentiable function and divided difference admissible function, we establish the existence of any sequence generated by the Newton-like method and prove that the sequence generated by this method converges linearly and superlinearly to a solution of the variational inclusion. Specifically, when the Frechet derivative of the differentiable function is continuous, Lipschitz continuous, divided difference admissible function admits first order divided di_erence and the setvalued mapping is pseudo-Lipschitz continuous, we show the linear and superlinear convergence of the method.

GANIT J. Bangladesh Math. Soc.Vol. 40 (2020) 43-53