Strong Convergence of Self-adaptive Inertial Algorithms for Solving Split Variational Inclusion Problems with Applications

In this paper, four self-adaptive iterative algorithms with inertial effects are introduced to solve a split variational inclusion problem in real Hilbert spaces. One of the advantages of the suggested algorithms is that they can work without knowing the prior information of the operator norm. Strong convergence theorems of these algorithms are established under mild and standard assumptions. As applications, the split feasibility problem and the split minimization problem in real Hilbert spaces are studied. Finally, several preliminary numerical experiments as well as an example in the field of compressed sensing are proposed to support the advantages and efficiency of the suggested methods over some existing ones.

Automated summary

This paper introduces four self-adaptive iterative algorithms with inertial effects for solving a split variational inclusion problem in real Hilbert spaces. These algorithms have the advantage of being able to work without prior information of the operator norm, and strong convergence theorems are established under mild and standard assumptions. Applications include studying the split feasibility problem and split minimization problem in real Hilbert spaces, supported by preliminary numerical experiments and an example in the field of compressed sensing.