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

2019/11/05 by Guangyu Gao, Bo Han, Gao, Guangyu +3
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Photoacoustic and Ultrasonic Imaging #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.1911.01728

openalex publication_date 2019/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Sequential subspace optimization for nonlinear inverse problems
• Regularization of inverse problems by two-point gradient methods with convex constraints
• Convergence of the gradient method for ill-posed problems
• Iterative regularization of parameter identification problems by sequential quadratic programming methods
• On the Convergence of Stochastic Gradient Descent for Nonlinear Ill-Posed Problems