An accelerated forward-backward-half forward splitting algorithm for monotone inclusion with applications to image restoration

Inertial methods play a vital role in accelerating the convergence speed of optimization algorithms. We present an inertial forward-backward-half forward splitting algorithm, which mainly finds a zero of the sum of three operators, where two of them are cocoercive operator and monotone-Lipschitz continuous respectively. Meanwhile, the convergence analysis of the proposed algorithm is established under mild conditions. To overcome the difficulty in the calculation for the resolvent of the composite operator, relying on a primal-dual idea, we expand the proposed algorithm to solve the composite inclusion problem involving a linearly composed monotone operator. As an application, we make use of the obtained inertial algorithm to deal with a composite convex optimization problem. We also show extensive numerical experiments on the total variation-based image deblurring problem to demonstrate the efficiency of the proposed algorithm. Specifically, the proposed algorithm not only has a better quality of the deblurring image but also converges more rapidly than the original one.