BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Hedy Attouch (University of Montpellier) DTSTART:20210118T143000Z DTEND:20210118T153000Z DTSTAMP:20260423T035035Z UID:OWOS/32 DESCRIPTION:Title: Ac celeration of First-Order Optimization Algorithms via Inertial Dynamics wi th Hessian Driven Damping\nby Hedy Attouch (University of Montpellier) as part of One World Optimization seminar\n\n\nAbstract\nIn a Hilbert spa ce\, for convex optimization\, we report on recent advances regarding the acceleration of first-order algorithms. We rely on inertial dynamics with damping driven by the Hessian\, and the link between continuous dynamic sy stems and algorithms obtained by temporal discretization. We first review the classical results\, from Polyak's heavy ball with friction method to N esterov's accelerated gradient method. Then we introduce the damping drive n by the Hessian which intervenes in the dynamic in the form $\\nabla^2f(x (t))\\dot{x}(t)$. By treating this term as the time derivative of $\\nabla f(x(t))$\, this gives\, in discretized form\, first-order algorithms. As a fundamental property\, this geometric damping makes it possible to atten uate the oscillations. In addition to the fast convergence of the values\, the algorithms thus obtained show a rapid convergence towards zero of the gradients. The introduction of time scale factors further accelerates the se algorithms. On the basis of a regularization technique using the Moreau envelope\, we extend the method to non-smooth convex functions with exten ded real values. Numerical results for structured optimization problems su pport our theoretical findings. Finally\, we evoke recent development conc erning the extension of these results to the case of general monotone incl usions\, inertial ADMM algorithms\, dry friction\, inexact/stochastic case \, thus showing the versatility of the method.\n\nThis lecture is based on the recent collaborative article:\nH. Attouch\, Z. Chbani\, J. Fadili\, H . Riahi\, First-order optimization algorithms via inertial systems with H essian driven damping\, Math. Program.\, (2020)\, https://doi.org/10.1007/ s10107-020-01591-1\, preprint available at hal-02193846.\n\nThe address a nd password of the zoom room of the seminar are sent by e-mail on the mail inglist of the seminar one day before each talk\n LOCATION:https://researchseminars.org/talk/OWOS/32/ END:VEVENT END:VCALENDAR