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Modified parallel projection methods for the multivalued lexicographic variational inequalities using proximal operator in Hilbert spaces
Author(s) -
Ngoc Anh Pham,
Thi Hoai An Le
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6118
Subject(s) - mathematics , variational inequality , hilbert space , lipschitz continuity , lexicographical order , monotone polygon , projection (relational algebra) , convergence (economics) , operator (biology) , projection method , pure mathematics , algorithm , dykstra's projection algorithm , combinatorics , geometry , chemistry , biochemistry , repressor , transcription factor , economics , gene , economic growth
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.