A primal-dual splitting algorithm for monotone inclusions with applications

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.