Parallel inertial forward–backward splitting methods for solving variational inequality problems with variational inclusion constraints

The inertial forward–backward splitting algorithm can be considered as a modified form of the forward–backward algorithm for variational inequality problems with monotone and Lipschitz continuous cost mappings. By using parallel and inertial techniques and the forward–backward splitting algorithm, i...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences Vol. 48; no. 1; pp. 748 - 764
Main Authors: Thang, Tran Van, Tien, Ha Manh
Format: Journal Article
Language:English
Published: Freiburg Wiley Subscription Services, Inc 15.01.2025
Subjects:
Algorithms
Constraints
forward–backward splitting method
Hilbert space
inertial technique
monotonicity
resolvent operator
Splitting
variational inequality problem
ISSN:0170-4214, 1099-1476
Online Access:Get full text
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Summary:The inertial forward–backward splitting algorithm can be considered as a modified form of the forward–backward algorithm for variational inequality problems with monotone and Lipschitz continuous cost mappings. By using parallel and inertial techniques and the forward–backward splitting algorithm, in this paper, we propose a new parallel inertial forward–backward splitting algorithm for solving variational inequality problems, where the constraints are the intersection of common solution sets of a finite family of variational inclusion problems. Then, strong convergence of proposed iteration sequences is showed under standard assumptions imposed on cost mappings in a real Hilbert space. Finally, some numerical experiments demonstrate the reliability and benefits of the proposed algorithm.
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ISSN:0170-4214
1099-1476
DOI:10.1002/mma.10356