22 citations · 38 across the 9 of their papers we have counts for
5 papers · 1 filter
On the Convergence of Proximal Algorithms for Weakly-convex Min-max Optimization
Guido Tapia-Riera, Camille Castera, Nicolas Papadakis
We study alternating first-order algorithms with no inner loops for solving nonconvex-strongly concave min-max problems. We show the convergence of the alternating gradient descent…
Accelerated Gradient Dynamics on Riemannian Manifolds: Faster Rate and Trajectory Convergence
Tejas Natu, Camille Castera, Jalal Fadili +1
In order to minimize a differentiable geodesically convex function, we study a second-order dynamical system on Riemannian manifolds with an asymptotically vanishing damping term o…
Near-optimal Closed-loop Method via Lyapunov Damping for Convex Optimization
Severin Maier, Camille Castera, Peter Ochs
We introduce an autonomous system with closed-loop damping for first-order convex optimization. While, to this day, optimal rates of convergence are almost exclusively achieved by…
Continuous Newton-like Methods featuring Inertia and Variable Mass
Camille Castera, Hedy Attouch, Jalal Fadili +1
We introduce a new dynamical system, at the interface between second-order dynamics with inertia and Newton's method. This system extends the class of inertial Newton-like dynamics…
Inertial Newton Algorithms Avoiding Strict Saddle Points
Camille Castera
We study the asymptotic behavior of second-order algorithms mixing Newton's method and inertial gradient descent in non-convex landscapes. We show that, despite the Newtonian behav…