2015/03/18 by Yi Zhou, Zhou, Yi, Yingbin Liang +3
Computer Science · Engineering · Mathematics · #Algorithm #Applied mathematics #Backtracking #Bregman divergence #Computer science #Convergence (economics) #Convex optimization #FOS: Mathematics #Geometry #Line (geometry) #Line search #Mathematical optimization #Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Proximal Gradient Methods #Regular polygon #Simple (philosophy) #Sparse and Compressive Sensing Techniques #math.OC
paper · pdf · doi:10.48550/arxiv.1503.05601
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2015/03/18 · arxiv created 2017/12/17 · arxiv updated 2017/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08
In this paper, we provide a simple convergence analysis of proximal gradient algorithm with Bregman distance, which provides a tighter bound than existing result. In particular, for the problem of minimizing a class of convex objective functions, we show that proximal gradient algorithm with Bregman distance can be viewed as proximal point algorithm that incorporates another Bregman distance. Consequently, the convergence result of the proximal gradient algorithm with Bregman distance follows directly from that of the proximal point algorithm with Bregman distance, and this leads to a simpler convergence analysis with a tighter convergence bound than existing ones. We further propose and analyze the backtracking line search variant of the proximal gradient algorithm with Bregman distance. Simulation results show that the line search method significantly improves the convergence performance of the algorithm.