An accelerated conjugate method for split variational inclusion problems with applications

In this work, split variational inclusion problems were investigated by combining new stepsizes and inertia with conjugate gradient methods in real Hilbert spaces, in which the inertial steps were used to speed up the convergent rate of the methods, and the new stepsizes not only avoided computing the operator norm, but also ensured that the strong convergence of the methods holds without Lipschitz continuity of the monotone operator. Also, the proximal operator was computed less than that in the original method. Further, the split feasibility and split minimization problems were considered. Finally, several examples were used for illustration and comparison.