SIPo: Fast Optimization Algorithms from a Continuous Dynamics Perspective

Abstract:

This talk presents fast optimization algorithms from the viewpoint of continuous dynamical systems.

We begin with the classical correspondence between gradient flow and gradient descent, and then discuss how nonsmooth gradient flows naturally lead to proximal-type methods. The main focus is on inertial dynamical systems, where second-order terms introduce memory and momentum into the optimization process.

Through this perspective, we explain how continuous-time models such as the heavy-ball system and Nesterov-type dynamics provide insight into acceleration, damping, stability, and convergence of fast first-order methods.

We also discuss how these ideas can be extended beyond standard minimization problems, including recent directions for nonconvex minimax optimization.

Speaker: Raúl Tintaya (CMM, U. de Chile)