Modified parallel projection methods for the multivalued lexicographic variational inequalities using proximal operator in Hilbert spaces |
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Authors: | Pham Ngoc Anh Le Thi Hoai An |
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Institution: | 1. Institute for Research and Applications of Optimization, VinTech, Vingroup, Ha Noi, Vietnam;2. Institute for Research and Applications of Optimization, VinTech, Vingroup, Ha Noi, Vietnam
Univeristy of Lorraine, France |
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Abstract: | 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. |
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Keywords: | demicontractive mappings Lipschitz continuous monotone projection methods multivalued lexicographic variational inequalities proximal operator |
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