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math.OC2026
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…
math.OC2024
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…