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Least-time Gradient Flow

arXiv:2610. 01426v1 Announce Type: new Abstract: Prescribing the speed of gradient flow on the risk itself, by the dynamics $\dot w=-u(E(w))\nabla E(w)/\abs{\nabla E(w)}^{2}$, makes the risk $e(t)=E(w(t))$ obey $\dot e=-u(e)$ exactly, whatever the landscape~$E$; the time needed to reach zero risk from $e_0$ is $\int_0^{e_0}\dd e/u(e)$.

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Nonmonotone subgradient methods based on a local descent lemma

arXiv:2510. 19341v3 Announce Type: replace-cross Abstract: In this paper we present a nonmonotone line search subgradient algorithm tailored to upper-$\mathcal{C}^2$ functions.

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Nonconvex Composite Functional Constraints via First-Order Augmented Lagrangian Methods under Local Regularity

arXiv:2607. 08954v1 Announce Type: cross Abstract: We study nonasymptotic convergence of primal-dual methods for a class of nonconvex constrained optimization problems with a convex-composite structure.

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