Convergence of projection and contraction algorithms with outer perturbations and their applications to sparse signals recovery

In this paper, we study the bounded perturbation resilience of projection and contraction algorithms for solving variational inequality (VI) problems in real Hilbert spaces. Under typical and standard assumptions of monotonicity and Lipschitz continuity of the VI’s associated mapping, convergence of the perturbed projection and contraction algorithms is proved. Based on the bounded perturbed resilience of projection and contraction algorithms, we present some inertial projection and contraction algorithms. In addition, we show that the perturbed algorithms converge at the rate of O(1 / t).