Inertial dynamics and algorithms for convex optimization

This research investigates the convergence properties of Nesterov's accelerated gradient method by viewing it through the lens of continuous inertial dynamics. By linking algorithms to second-order ordinary differential equations, the thesis first analyzes two inertial dynamical systems in convex optimization, uncovering fresh convergence results and expanding the models to smooth saddle point problems. It then examines two alternative versions of Nesterov's algorithm: one featuring an adaptive step size that avoids costly line searches, and another built on a less-studied backward-forward configuration.