New self-adaptive methods with double inertial steps for solving splitting monotone variational inclusion problems with applications

Abstract

In this paper, without the co-coerciveness assumption of the associated mappings, we show the iterative sequences generated by our new algorithms converge strongly to a solution of the splitting monotone variational inclusion problem in infinite dimensional real Hilbert spaces. The step sizes of the new algorithms are updated per iteration by a simple calculation without knowing the prior information of the operator norm. Some parameters are relaxed to enlarge the value range of the corresponding step sizes. Double inertial extrapolation steps are incorporated in the new algorithms to accelerate their convergence speed. As applications, the split variational inclusion problem, the monotone inclusion problem and the split variational inequality problem are studied. Some numerical experiments are performed to illustrate the computation efficiency of the new algorithms.