An inexact primal–dual method with correction step for a saddle point problem in image debluring

Changjie Fang (), Liliang Hu and Shenglan Chen
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Changjie Fang: Chongqing University of Posts and Telecommunications
Liliang Hu: Chongqing University of Posts and Telecommunications
Shenglan Chen: Chongqing University of Posts and Telecommunications

Journal of Global Optimization, 2023, vol. 87, issue 2, No 27, 965-988

Abstract: Abstract In this paper, we present an inexact primal–dual method with correction step for a saddle point problem by introducing the notations of inexact extended proximal operators with symmetric positive definite matrix D. Relaxing requirement on primal–dual step sizes, we prove the convergence of the proposed method. We also establish the O(1/N) convergence rate of our method in the ergodic sense. Moreover, we apply our method to solve TV- $$\hbox {L}_1$$ L 1 image deblurring problems. Numerical simulation results illustrate the efficiency of our method.

Keywords: Primal–dual method; Inexact extended proximal operators; Convergence rate; Prediction and correction; Image deblurring (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10898-022-01211-6

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