| Abstract: |
| 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, cocoercive terms, and composite monotone operators involving linear mappings. The algorithm combines forward evaluations for the cocoercive components with backward steps for the monotone operators, and incorporates a dual update to handle the linear composition term. Our framework generalizes and unifies several existing methods, while requiring only a single resolvent or operator evaluation per iteration, thereby maintaining computational efficiency. We establish weak convergence of the generated iterates under standard assumptions on monotonicity and cocoercivity. Furthermore, strong convergence is guaranteed under a mild regularity condition, such as uniform monotonicity. Finally, we present numerical experiments on structured convex and nonconvex optimization problems arising in image deblurring and denoising, which demonstrate the practical efficiency and flexibility of the proposed approach. |
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