Third order dynamical systems for the sum of two generalized monotone operators
Third order dynamical systems for the sum of two generalized monotone operators
In this paper, we propose and analyze a third-order dynamical system for finding zeros of the sum of two generalized operators in a Hilbert space H. We establish the existence and uniqueness of the trajectories generated by the system under appropriate continuity conditions, and prove exponential convergence to the unique zero when the sum of the operators is strongly monotone. Additionally, we derive an explicit discretization of the dynamical system, which results in a forward–backward algorithm with double inertial effects and larger range of stepsize. We establish the linear convergence of the iterates to the unique solution using this algorithm. Furthermore, we provide convergence analysis for the class of strongly pseudo-monotone variational inequalities. We illustrate the effectiveness of our approach by applying it to structured optimization and pseudo-convex optimization problems.
47J20, 49J40, 90C30, 90C52, Dynamical system, Exponential convergence, Generalized monotonicity, Linear convergence, Monotone inclusion, Variational inequality
519-553
Hai, Pham Viet
5ff73de3-b38b-4fc4-9bc7-c0b62da6d32a
Vuong, Phan Tu
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
3 June 2024
Hai, Pham Viet
5ff73de3-b38b-4fc4-9bc7-c0b62da6d32a
Vuong, Phan Tu
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
Hai, Pham Viet and Vuong, Phan Tu
(2024)
Third order dynamical systems for the sum of two generalized monotone operators.
Journal of Optimization Theory and Applications, 202 (2), .
(doi:10.1007/s10957-024-02437-y).
Abstract
In this paper, we propose and analyze a third-order dynamical system for finding zeros of the sum of two generalized operators in a Hilbert space H. We establish the existence and uniqueness of the trajectories generated by the system under appropriate continuity conditions, and prove exponential convergence to the unique zero when the sum of the operators is strongly monotone. Additionally, we derive an explicit discretization of the dynamical system, which results in a forward–backward algorithm with double inertial effects and larger range of stepsize. We establish the linear convergence of the iterates to the unique solution using this algorithm. Furthermore, we provide convergence analysis for the class of strongly pseudo-monotone variational inequalities. We illustrate the effectiveness of our approach by applying it to structured optimization and pseudo-convex optimization problems.
Text
s10957-024-02437-y
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Accepted/In Press date: 4 April 2024
Published date: 3 June 2024
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Publisher Copyright:
© The Author(s) 2024.
Keywords:
47J20, 49J40, 90C30, 90C52, Dynamical system, Exponential convergence, Generalized monotonicity, Linear convergence, Monotone inclusion, Variational inequality
Identifiers
Local EPrints ID: 491770
URI: http://eprints.soton.ac.uk/id/eprint/491770
ISSN: 0022-3239
PURE UUID: 83afe611-69e0-425d-91b5-4a2b9b1f7e00
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Date deposited: 03 Jul 2024 17:24
Last modified: 28 Aug 2024 01:59
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Author:
Pham Viet Hai
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