A Generalization of the Chambolle-Pock Algorithm to Banach Spaces with Applications to Inverse Problems

2014/11/29 by Thorsten Hohage, Hohage, Thorsten, C. Homann +1
Computer Science · Engineering · Mathematics · #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Optimization and Variational Analysis #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.1412.0126

openalex publication_date 2014/11/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

For a Hilbert space setting Chambolle and Pock introduced an attractive first-order algorithm which solves a convex optimization problem and its Fenchel dual simultaneously. We present a generalization of this algorithm to Banach spaces. Moreover, under certain conditions we prove strong convergence as well as convergence rates. Due to the generalization the method becomes efficiently applicable for a wider class of problems. This fact makes it particularly interesting for solving ill-posed inverse problems on Banach spaces by Tikhonov regularization or the iteratively regularized Newton-type method, respectively.

Citations

• On the convergence rate improvement of a primal-dual splitting algorithm\n for solving monotone inclusion problems

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