28 citations · 71 across the 18 of their papers we have counts for
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Continuized Nesterov Momentum Achieves the Complexity in Smooth Nonconvex Optimization
Julien Hermant, Jean-François Aujol, Charles Dossal +3
For first-order optimization of non-convex functions with Lipschitz-continuous gradient and Hessian, the best-known complexity for reaching an -approximation of a stat…
Continuized Nesterov Acceleration for Non-Convex Optimization
Julien Hermant, Jean-François Aujol, Charles Dossal +2
In convex optimization, continuous-time counterparts have been a fruitful tool for analyzing momentum algorithms. Fewer such examples are available when the function to minimize is…
Gradient correlation is a key ingredient to accelerate SGD with momentum
Julien Hermant, Marien Renaud, Jean-François Aujol +2
Empirically, it has been observed that adding momentum to Stochastic Gradient Descent (SGD) accelerates the convergence of the algorithm. However, the literature has been rather pe…
Strong Convergence of FISTA Iterates under H{ö}lderian and Quadratic Growth Conditions
Jean-François Aujol, Charles Dossal, Hippolyte Labarrière +1
Introduced by Beck and Teboulle, FISTA (for Fast Iterative Shrinkage-Thresholding Algorithm) is a first-order method widely used in convex optimization. Adapted from Nesterov's acc…
Heavy Ball Momentum for Non-Strongly Convex Optimization
Jean-François Aujol, Charles Dossal, Hippolyte Labarrière +1
When considering the minimization of a quadratic or strongly convex function, it is well known that first-order methods involving an inertial term weighted by a constant-in-time pa…
Parameter-Free FISTA by Adaptive Restart and Backtracking
Jean-François Aujol, Luca Calatroni, Charles Dossal +2
We consider a combined restarting and adaptive backtracking strategy for the popular Fast Iterative Shrinking-Thresholding Algorithm frequently employed for accelerating the conver…
Fast convergence of inertial dynamics with Hessian-driven damping under geometry assumptions
Jean-François Aujol, Charles Dossal, Văn Hào Hoàng +2
First-order optimization algorithms can be considered as a discretization of ordinary differential equations (ODEs) \cite{su2014differential}. In this perspective, studying the pro…
Optimal convergence rates for Nesterov acceleration
Jean François Aujol, Charles Dossal, Aude Rondepierre
In this paper, we study the behavior of solutions of the ODE associated to Nesterov acceleration. It is well-known since the pioneering work of Nesterov that the rate of convergenc…