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    STUDIA MATHEMATICA - Issue no. 1 / 2022  
         
  Article:   A RELAXED VERSION OF THE GRADIENT PROJECTION METHOD FOR VARIATIONAL INEQUALITIES WITH APPLICATIONS.

Authors:  NGUYEN THE VINH, NGO THI THUONG.
 
       
         
  Abstract:  
DOI: 10.24193/subbmath.2022.1.06

Published Online: 2022-03-10
Published Print: 2022-03-31
pp. 73-89

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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.

Keywords: Variational inequality, gradient projection method, strong convergence, LASSO problem, image deblurring problem.

Mathematics Subject Classification (2010): 47J20, 90C25, 90C30, 90C52.
 
         
     
         
         
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