Wenli Huang, Haiyang Li, Jigen Peng, Yuchao Tang, Huimin He, Simplified primal-dual forward-backward splitting algorithm for solving structured monotone inclusion with applications
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DOI: 10.23952/jnva.9.2025.6.06
Volume 9, Issue 6, 1 December 2025, Pages 927-945
Abstract. This paper addresses the challenge of finding a zero of a structured monotone inclusion, which is closely related to convex minimization problems in signal and image processing. By defining a suitable product space, the monotone inclusion problem is transformed into the sum of two maximally monotone operators, one of which is cocoercive. Based on the preconditioned forward-backward splitting algorithm, we propose a new primal-dual splitting algorithm with a simple structure and prove its convergence with appropriate parameter conditions. In contrast to existing primal-dual forward-backward splitting algorithms, the proposed algorithm uses fewer variables and employs a reduced amount of parameters. Furthermore, we apply the algorithm to solve a class of convex minimization problems. Numerical experiments demonstrate the effectiveness and robustness of the proposed algorithm for image denoising problems.
How to Cite this Article:
W. Huang, H. Li, J. Peng, Y. Tang, H. He, Simplified primal-dual forward-backward splitting algorithm for solving structured monotone inclusion with applications, J. Nonlinear Var. Anal. 9 (2025), 927-945.