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Akram Chahid Bagy, Zaki Chbani, Hassan Riahi, On the strong convergence of an inertial proximal algorithm with a time scale, Hessian-driven damping, and a Tikhonov regularization term

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DOI: 10.23952/jano.6.2024.2.06
Volume 6, Issue 2, 1 August 2024, Pages 249-269

 

Abstract. This paper concerns with convergence properties of an inertial proximal algorithm that contains a Tikhonov term regularization, time scale parameter, and a Hessian-driven damping in a Hilbert space. More precisely, we prove the strong convergence of the proximal algorithm obtained by temporal discretization of a continuous dynamic that we treated earlier in a previous work. We also obtain the convergence of the values to the global minimum of the objective function, and a strong convergence of the gradient and the velocity towards zero. Finally, we present a numerical example to illustrate our results.

 

How to Cite this Article:
A.C. Bagy, Z. Chbani, H. Riahi, On the strong convergence of an inertial proximal algorithm with a time scale, Hessian-driven damping, and a Tikhonov regularization term, J. Appl. Numer. Optim. 6 (2024), 249-269.