arXiv:2608. 21359v1 Announce Type: cross Abstract: We develop a new direct accelerated Newton method for minimizing convex functions with Lipschitz continuous Hessian.
arXiv:2610.33516v1 Announce Type: new Abstract: Modern gradient boosting algorithms are based on Newton's method, which excels empirically but lacks global convergence guarantees. While recent work o...
arXiv:2610. 35195v1 Announce Type: cross Abstract: We develop and analyze multilevel gradient-regularized Newton methods for unconstrained convex optimization with Lipschitz-continuous Hessians.
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.
arXiv:2503. 04712v3 Announce Type: replace-cross Abstract: We study the optimization of non-convex functions that are not necessarily smooth (gradient and/or Hessian are Lipschitz) using first order methods.
arXiv:2608.22129v2 Announce Type: replace Abstract: Cubic regularized Newton methods have the optimal $\mathcal{O}(\epsilon^{-3/2})$ global rate, but a dense subproblem solve limits the feasible bloc...
arXiv:2608. 12665v1 Announce Type: cross Abstract: For solving nonconvex equality-constrained optimization problems, a recent Gradient-Eigenstep Algorithm by Goyens et al.
arXiv:2209. 03282v5 Announce Type: replace-cross Abstract: Accelerating the convergence of second-order optimization, particularly Newton-type methods, remains a pivotal challenge in algorithmic research.
arXiv:2307.07030v4 Announce Type: replace-cross Abstract: This paper considers the problem of understanding the behavior of a general class of accelerated gradient methods on smooth nonconvex functio...
arXiv:2509.02894v2 Announce Type: replace-cross Abstract: We propose an inexact proximal augmented Lagrangian method (P-ALM) for nonconvex structured optimization problems. The proposed method featur...
arXiv:2406. 13041v3 Announce Type: replace Abstract: Lower-bound analyses for nonconvex strongly-concave minimax optimization problems have shown that stochastic first-order algorithms require at least $\mathcal{O}(\varepsilon^{-4})$ sample complexity to find an $\varepsilon$-stationary point.
The paper introduces Split-Client, a task‑parallel scheme that separates Hessian factorization (performed by a curvature client in the background) from gradient updates (performed by a gradient client using the latest available Hessian). It proves that the resulting first‑order stationarity bound depends on the average age of the curvature matrix rather than its maximum, and extends this analysis to subsampled and inexact Hessians. Experiments on two LIBSVM datasets show that this approach reduces the objective faster in wall‑clock time than both Lazy and Vanilla cubic Newton, especially at intermediate accuracy levels.
arXiv:2605.04722v2 Announce Type: replace-cross Abstract: Input convex neural networks (ICNNs) are used to learn convex objectives whose minimizers define decisions, making efficient and reliable opt...