Tikhonov Regularized Exterior Penalty Dynamics for Constrained Variational Inequalities

Solving equilibrium problems under constraints is an important problem in optimization and optimal control. In this context an important practical challenge is the efficient incorporation of constraints. We develop a continuous-time method for solving constrained variational inequalities based on a...

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Bibliographic Details
Published in:IEEE control systems letters 2024, Vol.8, p.622-627
Main Authors: Staudigl, Mathias, Qu, Siqi
Format: Article
Language:English
Subjects:
Constrained control
Convergence
Dynamical systems
Games
Hilbert space
Lyapunov methods
Nash equilibrium
optimization
time-varying systems
Trajectory
variational methods
Vectors
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Summary:Solving equilibrium problems under constraints is an important problem in optimization and optimal control. In this context an important practical challenge is the efficient incorporation of constraints. We develop a continuous-time method for solving constrained variational inequalities based on a new penalty regulated dynamical system in a general potentially infinite-dimensional Hilbert space. In order to obtain strong convergence of the issued trajectory of our method, we incorporate an explicit Tikhonov regularization parameter in our method, leading to a class of time-varying monotone inclusion problems featuring multiscale aspects. Besides strong convergence, we illustrate the practical efficiency of our developed method in solving constrained min-max problems.
ISSN:2475-1456
2475-1456
DOI:10.1109/LCSYS.2024.3401019