Modified parallel projection methods for the multivalued lexicographic variational inequalities using proximal operator in Hilbert spaces
Phạm Ngọc Ánh, Hoai An Le Thi · Mathematical Methods in the Applied Sciences · 2019
In this paper, building upon projection methods and parallel splitting‐up techniques with using proximal operators, we propose new algorithms for solving the multivalued lexicographic variational inequalities in a real Hilbert space. First, the strong convergence theorem is shown with Lipschitz continuity of the cost mapping, but it must satisfy a strongly monotone condition. Second, the convergent results are also established to the multivalued lexicographic variational inequalities involving a finite system of demicontractive mappings under mild assumptions imposed on parameters. Finally, some numerical examples are developed to illustrate the behavior of our algorithms with respect to existing algorithms.