A relaxed version of the gradient projection method for variational inequalities with applications
DOI:
https://doi.org/10.24193/subbmath.2022.1.06Keywords:
Variational inequality, gradient projection method, strong convergence, LASSO problem, image deblurring problem.Abstract
In this paper, we propose a relaxed version of the gradient projection method for strongly monotone variational inequalities defined on a level set of a (possibly non-differentiable) convex function. Our algorithm can be implemented easily since it computes on every iteration one projection onto some half-space containing the feasible set and only one value of the underlying mapping. Under mild and standard conditions we establish the strong convergence of the proposed algorithm. Numerical results and comparisons for the image deblurring problem show that our method can outperform related algorithms in the literature.
Mathematics Subject Classification (2010): 47J20, 90C25, 90C30, 90C52.
Received 20 December 2021; Revised 07 February 2022; Accepted 08 February 2022.
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