A fast two-point gradient algorithm based on sequential subspace optimization method for nonlinear ill-posed problems

TL;DR

This paper introduces a rapid two-point gradient algorithm based on sequential subspace optimization for nonlinear ill-posed problems, demonstrating improved efficiency and convergence through theoretical analysis and numerical simulations.

Contribution

It presents a novel two-point gradient method with systematic parameter selection and provides comprehensive convergence analysis for solving nonlinear ill-posed problems.

Findings

Significant reduction in iteration numbers

Decreased overall computational time

Effective for inverse potential problems

Abstract

In this paper, we propose and analyze a fast two-point gradient algorithm for solving nonlinear ill-posed problems, which is based on the sequential subspace optimization method. A complete convergence analysis is provided under the classical assumptions for iterative regularization methods. The design of the two-point gradient method involves the choices of the combination parameters which is systematically discussed. Furthermore, detailed numerical simulations are presented for inverse potential problem, which exhibit that the proposed method leads to a strongly decrease of the iteration numbers and the overall computational time can be significantly reduced.