Solving common variational inequalities by hybrid inertial parallel
subgradient extragradient-line algorithm for application to image
deblurring
Abstract
In this paper, we propose hybrid inertial parallel subgradient
extragradient-line algorithm for approximating a common solution of
variational inequality problems with monotone and $L$-Lipschitz
continuous mappings but $L$ is unknown and prove strong convergence
under some mild conditions in Hilbert space. We then give numerical
examples to demonstrate the performance of our algorithms better than
some of the algorithms mentioned in the literature. The novelty of our
algorithm is that we have shown the algorithm is resilient and has good
quality when the number of subproblems is large, the algorithm can be
applied to solve image deblurring when an image has common types of blur
effects.