An adaptive heavy ball method for ill-posed inverse problems

2024/04/04 by Qinian Jin, Jin, Qinian, Huang, Qin · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2404.03218

openalex publication_date 2024/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we consider ill-posed inverse problems, both linear and nonlinear, by a heavy ball method in which a strongly convex regularization function is incorporated to detect the feature of the sought solution. We develop ideas on how to adaptively choose the step-sizes and the momentum coefficients to achieve acceleration over the Landweber-type method. We then analyze the method and establish its regularization property when it is terminated by the discrepancy principle. Various numerical results are reported which demonstrate the superior performance of our method over the Landweber-type method by reducing substantially the required number of iterations and the computational time.

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