An inertial parallel CQ subgradient extragradient method for variational inequalities application to signal-image recovery

Abstract

In this paper, we introduce an inertial parallel CQ subgradient extragradient method for nding a common solutions of variational inequality problems. The novelty of this paper is using linesearch methods to nd unknown L constant of L-Lipschitz continuous mappings. Strong convergence theorem has been proved under some suitable conditions in Hilbert spaces. Finally, we show applications to signal and image recovery, and show the good eciency of our proposed algorithm when the number of subproblems is increasing.

New Convergence Theorems for Pseudomonotone Variational Inequality on Hadamard Manifolds

“…The main advantages of these extensions are that non-convex problems and constrained problems in spaces with linear structure and symmetry may be transformed into convex problems and unconstrained problems on Hadamard manifolds without linear structure, respectively. So, many nonlinear problems on symmetric Hadamard manifolds have been attracted and studied by some authors, see for example [19][20][21][22][23][24][25][26][27][28][29] and the reference therein.…”