In cadrul seminarului de cercetare Analiza si Optimizare, de joi 08.06.2023, ora 12.30, va avea loc prezentarea cu titlul:

Fast continuous time approaches for convex nonsmooth optimization using Tikhonov regularization technique

susținută de către drd. Mikhail Karapetyants  (Universitatea din Viena), in colaborare cu Prof. dr. habil. Radu I. Bot  si Dr. Habil. Robert E. Csetnek (Universitatea din Viena).

Prezentarea va avea loc pe platforma ZOOM la adresa:

https://zoom.us/j/98704786553?pwd=RXBCYy9GRjBTK0RTM2QxbkV4NFVudz09

Meeting ID: 987 0478 6553
Passcode: optimizare

Abstract: In a Hilbert setting we study a second order in time differential equation, combining viscous and Hessian-driven damping, containing (optionally) a time scaling parameter function and a Tikhonov regularization term. The dynamical system is related to the problem of minimization of a nonsmooth convex function. In the formulation of the problem as well as in our analysis we use the Moreau envelope of the objective function and its gradient and heavily rely on their properties. We show that there is a setting where the system preserves and even improves the well-known fast convergence properties of the function and Moreau envelope along the trajectories and also of the gradient of Moreau envelope due to the presence of time scaling. Moreover, we prove strong convergence of the trajectories to the element of the minimal norm from the set of all minimizers of the objective. The talk will be a brief overview of the well-known results in this area concluding with the presentation of our contribution to this topic, including several numerical examples.