An inertial method for solving generalized split feasibility problems over the solution set of monotone variational inclusions

Abstract

In this paper, we propose a new inertial extrapolation method for solving the generalized split feasibility problems over the solution set of monotone variational inclusion problems in real Hilbert spaces. We prove that the proposed method converges strongly to a solution to the aforementioned problem under the assumption that the associated singlevalued operator for the monotone variational inclusion problem is monotone and Lipschitz continuous. Our method uses a stepsize that is generated at each iteration by some simple computations, which allows it to be easily implemented without the prior knowledge of the Lipschitz constant of the singlevalued operator. Moreover, we discuss some consequences of our results and apply them to solve the split linear inverse problems, for which we also considered a special case of the split linear inverse problem, namely, the LASSO problem. We also give some numerical illustrations of the proposed method in comparison with other method in the literature to further demonstrate the applicability and efficiency of our method.