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:2608. 08463v1 Announce Type: cross Abstract: We study second- and higher-order methods for solving smooth monotone variational inequalities (MVI).
By Lesi Chen, Xinliang Zhang, Hengyu Wang, Chengchang Liu, Yongchao Chen, Jingzhao Zhang
arXiv:2609. 23557v1 Announce Type: cross Abstract: We study second- and higher-order methods for solving smooth monotone variational inequalities (MVI).
By Xinliang Zhang, Lesi Chen, Linxuan Pan, Chengchang Liu, Junchi Yang, Jingzhao Zhang
arXiv:2609. 17973v1 Announce Type: cross Abstract: We introduce a new single-loop algorithmic framework for smooth nonconvex--concave minimax optimization.
By Minghao Zhang, Zi Xu
arXiv:2504.09409v3 Announce Type: replace-cross
Abstract: In this paper, we study nonconvex constrained stochastic zeroth-order optimization problems with exact constraints and stochastic objective e...
By Qiankun Shi, Han Yuan, Xiao Wang, Hao Wang
arXiv:2606. 05438v1 Announce Type: new Abstract: We study the deterministic first-order oracle complexity of finding \(\epsilon\)-stationary points in smooth nonconvex optimization when the objective satisfies higher-order smoothness assumptions.
By Dongruo Zhou
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
In this work, we study the oracle complexity of finding an $ε$-stationary point for nonconvex-strongly-convex (NC-SC) bilevel optimization using only first-order oracles. Existing methods achieving th...
arXiv:2502.21099v3 Announce Type: replace-cross
Abstract: This paper proposes {\sf AEPG-SPIDER}, an Adaptive Extrapolated Proximal Gradient (AEPG) method with variance reduction for minimizing compos...
By Ganzhao Yuan
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.
By Linglingzhi Zhu, Jiajin Li
arXiv:2511.02821v2 Announce Type: replace-cross
Abstract: We develop new accelerated first-order algorithms in the Frank-Wolfe (FW) family for minimizing smooth convex functions over compact convex s...
By Dan Garber
arXiv:2606. 20082v1 Announce Type: cross Abstract: The John ellipsoid of a symmetric polytope $P=\{\mathbf{x}\in\mathbb{R}^d:\|\mathbf{A}\mathbf{x}\|_\infty\le1\}$, $\mathbf{A}\in\mathbb{R}^{n\times d}$, is computed by a long line of leverage-score algorithms, from Cohen, Cousins, Lee and Yang (COLT 2019) to its successors [WY24, CLS+25], all reaching a $(1+\varepsilon)$-approximation in $\Theta(\varepsilon^{-1}\log(n/d))$ iterations.
By Xiaoyu Li, Junwei Yu, Jiaojiao Jiang, Junbin Gao, Andi Han