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

arXiv comment28 pages, 4 figures

References in corpus (4)

• Nesterov's Accelerated Gradient Method for Nonlinear Ill-Posed Problems with a Locally Convex Residual Functional
• A fast subspace optimization method for nonlinear inverse problems in Banach spaces with an application in parameter identification
• A CG-type method in Banach spaces with an application to computerized tomography
• Regularization of inverse problems by two-point gradient methods with convex constraints