69 citations · 316 across the 30 of their papers we have counts for
22 papers · 1 filter
Gradient extremals, talwegs, valleys, and directional alignment for generic gradient descent
Pascal Bégout, Jérôme Bolte, Thomas Mariotti +1
Gradient extremals are loci along which the gradient is an eigenvector of the Hessian. These objects provide a natural geometric framework connecting several notions, notably valle…
One-step differentiation of iterative algorithms
Jérôme Bolte, Edouard Pauwels, Samuel Vaiter
In appropriate frameworks, automatic differentiation is transparent to the user at the cost of being a significant computational burden when the number of operations is large. For…
Automatic differentiation of nonsmooth iterative algorithms
Jérôme Bolte, Edouard Pauwels, Samuel Vaiter
Differentiation along algorithms, i.e., piggyback propagation of derivatives, is now routinely used to differentiate iterative solvers in differentiable programming. Asymptotics is…
The Iterates of the Frank-Wolfe Algorithm May Not Converge
Jérôme Bolte, Cyrille W. Combettes, Édouard Pauwels
The Frank-Wolfe algorithm is a popular method for minimizing a smooth convex function over a compact convex set . While many convergence results have been derived…
Subgradient sampling for nonsmooth nonconvex minimization
Jérôme Bolte, Tam Le, Edouard Pauwels
Risk minimization for nonsmooth nonconvex problems naturally leads to first-order sampling or, by an abuse of terminology, to stochastic subgradient descent. We establish the conve…
Long term dynamics of the subgradient method for Lipschitz path differentiable functions
Jerome Bolte, Edouard Pauwels, Rodolfo Rios-Zertuche
We consider the long-term dynamics of the vanishing stepsize subgradient method in the case when the objective function is neither smooth nor convex. We assume that this function i…