A stochastic column-block gradient descent method for solving nonlinear systems of equations

TL;DR

This paper introduces a stochastic column-block gradient descent method for nonlinear systems, featuring an optimal step size and proven convergence, with numerical results showing superior performance over existing methods.

Contribution

The paper presents a novel stochastic gradient descent approach with an optimized step size for solving nonlinear equations, along with convergence analysis and empirical validation.

Findings

Outperforms existing methods in numerical experiments

Provides a convergence rate upper bound

Features an approximately optimal step size

Abstract

In this paper, we propose a new stochastic column-block gradient descent method for solving nonlinear systems of equations. It has a descent direction and holds an approximately optimal step size obtained through an optimization problem. We provide a thorough convergence analysis, and derive an upper bound for the convergence rate of the new method. Numerical experiments demonstrate that the proposed method outperforms the existing ones.