Inertial generalized proximal Peaceman–Rachford splitting method for separable convex programming

Abstract

The Peaceman–Rachford splitting method (PRSM) is a preferred method for solving the two-block separable convex minimization problems with linear constraints at present. In this paper, we propose an inertial generalized proximal PRSM (abbreviated as IGPRSM) to improve computing efficiency, which unify the ideas of inertial proximal point and linearization technique. Both subproblems are linearized by positive semi-definite proximal matrices, and we explain why the matrix cannot be indefinite. The global convergence and the worst-case asymptotic iteration complexity are derived theoretically via the variational inequality framework. Numerical experiments on LASSO, total variation (TV) based denoising models and image decomposition problems are presented to show the effectiveness of the introduced method even compared with the state-of-the-art methods.

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Acknowledgements

We would like to express our great appreciation to editors and anonymous referees for their valuable and constructive comments and suggestions on our manuscript. These comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. This work was supported by National Natural Science Foundation of China (No. 61877046).

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Correspondence to Zhao Deng.

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Deng, Z., Liu, S. Inertial generalized proximal Peaceman–Rachford splitting method for separable convex programming. Calcolo 58, 10 (2021). https://doi.org/10.1007/s10092-021-00399-5

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Keywords

  • Convex programming
  • Peaceman–Rachford splitting method
  • Inertial proximal point
  • Indefinite
  • Variational inequality
  • Global convergence

Mathematics Subject Classification

  • 90C25
  • 90C30
  • 94A08