A Newton conditional gradient method for constrained nonlinear systems

TL;DR

This paper introduces a novel algorithm combining Newton and conditional gradient methods for solving constrained nonlinear systems, with proven local convergence for broad classes of functions and supporting numerical experiments.

Contribution

It proposes a new Newton-conditional gradient algorithm with a unified convergence analysis applicable to diverse nonlinear functions.

Findings

Convergence established for functions with Holder-like derivatives.

Applicable to a broad subclass of analytic functions.

Numerical experiments demonstrate effectiveness and compare favorably with existing methods.

Abstract

In this paper, we consider the problem of solving a constrained system of nonlinear equations. We propose an algorithm based on a combination of the Newton and conditional gradient methods, and establish its local convergence analysis. Our analysis is set up by using a majorant condition technique, allowing us to prove in a unified way convergence results for two large families of nonlinear functions. The first one includes functions whose derivative satisfies a Holder-like condition, and the second one consists of a substantial subclass of analytic functions. Numerical experiments illustrating the applicability of the proposed method are presented, and comparisons with some other methods are discussed.