Abstract
Recently, a globally convergent variant of Peaceman–Rachford splitting method (PRSM) has been proposed by He et al. In this paper, motivated by the idea of the generalized alternating direction method of multipliers, we propose, analyze and test a generalized PRSM for separable convex programming, which removes some restrictive assumptions of He’s PRSM. Furthermore, both subproblems are approximated by the linearization technique, and the resulting subproblems thus may have closed-form solution, especially in some practical applications. We prove the global convergence of the proposed method and report some numerical results about the image deblurring problems, which demonstrate that the new method is efficient and promising.
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Acknowledgments
The authors gratefully acknowledge the helpful comments and suggestions of the anonymous reviewers. This work is supported by the National Natural Science Foundation of China (71371139, 11302188), the Shanghai Shuguang Talent Project (13SG24), the Shanghai Pujiang Talent Project (12PJC069), the foundation of Scientific Research Project of Shandong Universities (J15LI11), and the foundation of Zaozhuang University (2014YB03).
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Sun, M., Liu, J. Generalized Peaceman-Rachford splitting method for separable convex programming with applications to image processing. J. Appl. Math. Comput. 51, 605–622 (2016). https://doi.org/10.1007/s12190-015-0922-6
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DOI: https://doi.org/10.1007/s12190-015-0922-6