A modified Newton-secant method for solving nonsmooth generalized equations

Abstract

In this paper, we study the solvability of nonsmooth generalized equations in Banach spaces using a modified Newton-secant method, by assuming a Hölder condition. Also, we generalize a Dennis-Moré theorem to characterize the superlinear convergence of the proposed method applied to nonsmooth generalized equations under strong metric subregularity. Numerical examples are provided to illustrate the effectiveness of our approach.

Keywords

• Newton-Kantorovich theorem
• divided differences
• Newton-secant method
• generalized equations