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

2013/03/12 by Radu Ioan Boţ, Bot, Radu Ioan, Ernö Robert Csetnek +3 · 2 citations
Computer Science · Engineering · Mathematics · #47H05 #65K05 #90C25 #Advanced Optimization Algorithms Research #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Optimization and Variational Analysis #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.1303.2875

openalex publication_date 2013/03/12 · openalex created_date 2022/08/13 · openalex updated_date 2026/07/28

Abstract

We present two modified versions of the primal-dual splitting algorithm\nrelying on forward-backward splitting proposed in citevu for solving\nmonotone inclusion problems. Under strong monotonicity assumptions for some of\nthe operators involved we obtain for the sequences of iterates that approach\nthe solution orders of convergence of O(1/n) and O(\ωⁿ), for \ω \∈\n(0,1), respectively. The investigated primal-dual algorithms are fully\ndecomposable, in the sense that the operators are processed individually at\neach iteration. We also discuss the modified algorithms in the context of\nconvex optimization problems and present numerical experiments in image\nprocessing and support vector machines classification.\n

Cited by

• A primal-dual splitting algorithm with convex combination and larger step sizes for composite monotone inclusion problems
• A Generalization of the Chambolle-Pock Algorithm to Banach Spaces with Applications to Inverse Problems

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