An inertial subgradient extragradient method of variational inequality problems involving quasi‐nonexpansive operators with applications

Abstract

In this work, a new algorithm is suggested to solve the variational inequality problems for Lipschitz continuous and monotone operators and the fixed point problems for quasi-nonexpansive operators. This algorithm is constructed based on the inertial subgradient extragradient method. In addition, a strong convergence theorem for this algorithm is obtained under some extra conditions. Furthermore, an application to a signal recovery in compressed sensing problem is shown as a numerical example of the algorithm. Additionally, another example in an infinite-dimensional space is given.