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A simple primal-dual algorithm for minimization of the sum of three convex functions

WANG Shuo1  ZHU Zhibin1,*  ZHANG Benxin2   

  1. 1. School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin~541004, Guangxi, China; 2. School of Electronic Engineering and Automation, Guangxi Key Laboratory of Automatic Detecting Technology and Instruments, Guilin University of Electronic Technology, Guilin~541004, Guangxi, China
  • Received:2018-01-08 Online:2018-06-15 Published:2018-06-15

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Abstract:

In this study, we propose a simple primal-dual algorithm for minimization of a sum of three convex separable functions, which are involved a smooth function with Lipschitz continuous gradient, a nonsmooth function and a linear composite nonsmooth function. A predictor-corrector scheme to the dual variable is used in our algorithm. Convergence and convergence rate are also discussed. In the end, numerical results illustrate the efficiency of this method.

Key words: primal-dual method, saddle-point problem, total variation, image reconstruction