This seminar is intended to talk about recent studies carried out on second-order differential systems and their temporal discretization (inertial algorithms) to solve convex minimization problems without constraint.
The main points of this talk:
• Convergence properties of the second continuous system comprising three coefficients varying with time: viscous damping coefficient, the Hessian driven damping coefficient, and the time scaling coefficient.
• Recent developments concerning the acceleration of first order algorithms with inertia and Hessian damping. Some numerical results are considered to show the fast convergence speeds obtained and the role of Hessian driven coefficient in the attenuation of oscillations.
• Advanced results of damped inertial dynamics with vanishing Tikhonov regularization: strong convergence of the trajectories towards the minimizer of minimum norm.