2023
DOI: 10.3934/eect.2022022
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On the effect of perturbations in first-order optimization methods with inertia and Hessian driven damping

Abstract: <p style='text-indent:20px;'>Second-order continuous-time dissipative dynamical systems with viscous and Hessian driven damping have inspired effective first-order algorithms for solving convex optimization problems. While preserving the fast convergence properties of the Nesterov-type acceleration, the Hessian driven damping makes it possible to significantly attenuate the oscillations. To study the stability of these algorithms with respect to perturbations, we analyze the behaviour of the correspondin… Show more

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Cited by 6 publications
(2 citation statements)
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“…considered by Alecsa-László-Pint ¸a in [11], see also Attouch-Fadili-Kungurtsev [25] in the perturbed case.…”
Section: Hessian-driven Dampingmentioning
confidence: 91%
See 1 more Smart Citation
“…considered by Alecsa-László-Pint ¸a in [11], see also Attouch-Fadili-Kungurtsev [25] in the perturbed case.…”
Section: Hessian-driven Dampingmentioning
confidence: 91%
“…considered by Alecsa, László, and Pint ¸a in [11], see also Attouch, Fadili, and Kungurtsev [25] in the perturbed case. The reason for referring to the approach as "implicit" stems from the fact that by utilizing Taylor expansion, as s approaches infinity and ẋ(s) approaches zero, one can approximate:…”
Section: Introducing (Drystar) By Scaling and Averaging Of (Drygrad)mentioning
confidence: 88%