Nesterov's Accelerated Gradient Method for Nonlinear Ill-Posed Problems with a Locally Convex Residual Functional

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 a convergence analysis for ill-posed problems of this method 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.

30 pages

References in corpus (3)

• The rate of convergence of Nesterov's accelerated forward-backward method is actually faster than $1/k^2$
• Lamé Parameter Estimation from Static Displacement Field Measurements in the Framework of Nonlinear Inverse Problems
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