The Inertial Proximal Algorithm for the Split Variational Inclusion Problem

In this work, we propose an inertial proximal splitting algorithm for the split variational inclusion problem in real Hilbert space, in which a new stepsize rule is provided for avoiding the case that the original stepsize equals to zero, It also helps enlarge the value range of the stepsize parameter. A weak and strong convergence theorem is established under mild conditions. Additionally, our obtained result is extended to split feasibility problems and split minimization problems. Finally, some numerical experiments are conducted to illustrate and compare.