Efficient primal-dual fixed point algorithm with dynamic stepsize for convex problems with applications to imaging restoration

2016/04/17 by Meng Wen, Shigang Yue, Wen, Meng +5
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Fixed Point Theorems Analysis #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1604.04852

openalex publication_date 2016/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the problem of finding the minimization of the sum of a convex function and the composition of another convex function with a continuous linear operator from the view of fixed point algorithms based on proximity operators. We design a primal-dual fixed point algorithm with dynamic stepsize based on the proximity operator and obtain a scheme with a closed form solution for each iteration. Based on Modified Mann iteration and the firmly nonexpansive properties of the proximity operator, we achieve the convergence of the proposed algorithm.

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