2026/01/01 by Changchi Huang, Jigen Peng, Liqian Qin +1 · 1 citation
Computer Science · Engineering · Mathematics · #Optimization and Variational Analysis #Sparse and Compressive Sensing Techniques #Numerical methods in inverse problems
paper · pdf · doi:10.3934/ipi.2026045
In this paper, we study a broad class of structured monotone inclusion problems in real Hilbert spaces. We propose a novel primal-dual splitting algorithm for solving such inclusions, which accommodates multiple monotone operators and cocoercive terms, as well as a composite monotone operator involving the linear map. The algorithm combines forward evaluations for the cocoercive components with backward resolvent steps for the monotone operators and employs a dual update for the linear composition term. It generalizes and unifies several existing methods, while requiring only a single resolvent or operator evaluation per iteration. We prove weak convergence of the iterates under standard assumptions on monotonicity and cocoercivity. Furthermore, we establish strong convergence under a mild regularity condition, such as uniform monotonicity. Numerical experiments on image deblurring and denoising problems demonstrate the efficiency and flexibility of the proposed algorithm.