An inertial subgradient extragradient method of variational inequality problems involving quasi‐nonexpansive operators with applications
Raweerote Suparatulatorn, Phakdi Charoensawan, Anchalee Khemphet · Mathematical Methods in the Applied Sciences · 2021
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.