The Linearized Bregman Method via Split Feasibility Problems: Analysis\n and Generalizations

2013/09/09 by Dirk A. Lorenz, Frank Schöpfer, Lorenz, Dirk A. +3 · 1 citation
Engineering · Mathematics · #65K10 #68U10 #90C25 #Advanced Optimization Algorithms Research #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Statistical and numerical algorithms

paper · pdf · doi:10.48550/arxiv.1309.2094

openalex publication_date 2013/09/09 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

The linearized Bregman method is a method to calculate sparse solutions to\nsystems of linear equations. We formulate this problem as a split feasibility\nproblem, propose an algorithmic framework based on Bregman projections and\nprove a general convergence result for this framework. Convergence of the\nlinearized Bregman method will be obtained as a special case. Our approach also\nallows for several generalizations such as other objective functions,\nincremental iterations, incorporation of non-gaussian noise models or box\nconstraints.\n

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