arXiv:2511. 22331v2 Announce Type: replace-cross Abstract: Bilevel optimization minimizes an objective function, defined by an upper-level problem whose feasible region is the solution of a lower-level problem.
By Lesi Chen, Jingzhao Zhang
arXiv:2511. 19656v3 Announce Type: replace Abstract: Although upper bound guarantees for bilevel optimization have been widely studied, progress on lower bounds has been limited due to the complexity of the bilevel structure.
By Kaiyi Ji
arXiv:2609. 23837v1 Announce Type: cross Abstract: We study the complexity of finding $(\delta,\epsilon)$-Goldstein stationary points of nonsmooth nonconvex Lipschitz functions.
By Guy Kornowski
The paper introduces the Anchored Extra-Proximal (AEP) framework for solving composite monotone inclusion problems, combining anchored extrapolation with an inexact anchored proximal update. By replacing the operator in the implicit update with its Taylor approximation and using a bisection line search, the authors derive a pth-order method that achieves a tangent-residual error ε in “~O(ε^{-2/(3p-1)})” oracle calls for every p ≥ 2. This complexity matches a proven lower bound, establishing the method as optimally efficient for deterministic algorithms in the pth-order oracle model.
arXiv:2609. 21880v1 Announce Type: cross Abstract: We study the optimization of convex objectives with $(L,\kappa-1)$-H\"older-continuous gradients in $\ell_q$ over $R B_p^d$, $1<\kappa\le 2$.
By David Mart\'inez-Rubio, Brian Bullins, Crist\'obal Guzm\'an, Mathieu Molina
arXiv:2609. 30212v1 Announce Type: cross Abstract: We study the deterministic oracle complexity of finding approximate solutions to composite monotone inclusion problems, formed by the sum of a smooth single-valued monotone operator and a maximally monotone set-valued operator, under the tangent-residual criterion.
By Ruichen Jiang, TaeHo Yoon