Nesterov's accelerated gradient method for nonlinear ill-posed problems with a locally convex residual functional. (12th July 2018)

• Record Type: Journal Article
• Authors: Hubmer, Simon; Ramlau, Ronny
• Is Part Of: Inverse problems. Volume 34:Number 9(2018:Sep.)
• Publication Date: 2018-07-12
• Subjects: Nesterov's accelerated gradient method -- Landweber iteration -- two-point gradient method -- regularization method -- inverse and ill-posed problems -- auto-convolution; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aacebe
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this paper, we consider Nesterov's accelerated gradient method for solving nonlinear inverse and ill-posed problems. Known to be a fast gradient-based iterative method for solving well-posed convex optimization problems, this method also leads to promising results for ill-posed problems. Here, we provide convergence analysis of this method for ill-posed problems based on the assumption of a locally convex residual functional. Furthermore, we demonstrate the usefulness of the method on a number of numerical examples based on a nonlinear diagonal operator and on an inverse problem in auto-convolution.