A simple convergence analysis of Bregman proximal gradient algorithm

Yi Zhou (), Yingbin Liang () and Lixin Shen ()
Additional contact information
Yi Zhou: Duke University
Yingbin Liang: The Ohio State University
Lixin Shen: Syracuse University

Computational Optimization and Applications, 2019, vol. 73, issue 3, No 7, 903-912

Abstract: Abstract 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.

Keywords: Proximal algorithms; Bregman distance; Convergence analysis; Line-search (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10589-019-00092-y

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