arXiv:2608. 08463v1 Announce Type: cross Abstract: We study second- and higher-order methods for solving smooth monotone variational inequalities (MVI).
arXiv:2609. 23557v1 Announce Type: cross Abstract: We study second- and higher-order methods for solving smooth monotone variational inequalities (MVI).
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.
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: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...
arXiv:2601. 21243v3 Announce Type: replace-cross Abstract: We consider max-min and min-max problems with objective functions that are possibly non-smooth, submodular with respect to the minimiser and concave with respect to the maximiser.
arXiv:2609. 20687v1 Announce Type: cross Abstract: We study first-order black-box convex optimization over an $\ell_p$-ball for objectives Lipschitz in the $\ell_q$-norm, solving in the affirmative the nonsmooth version of the COLT open question (Guz15b) on whether the geometry of a smaller feasible set ($p < q$) can improve convergence rates in convex optimization, and matching prior lower bounds up to logarithmic factors.
arXiv:2405. 00914v4 Announce Type: replace-cross Abstract: We present in this paper novel accelerated fully first-order methods in \emph{Bilevel Optimization} (BLO).
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 $R B_p^d$, $1<\kappa\le 2$.
The paper introduces single-loop stochastic projected damped extragradient (SPDE) and its variance-reduced variant (VR-SPDE) for stochastic nonconvex–(strongly) concave minimax problems. It provides SFO complexity bounds for achieving game stationarity and optimization stationarity, improving upon previous multi-loop methods while maintaining a single-loop structure. The results claim the best-known SFO complexities for these stationarity criteria among single-loop stochastic first‑order methods.
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...
arXiv:2609. 17973v1 Announce Type: cross Abstract: We introduce a new single-loop algorithmic framework for smooth nonconvex--concave minimax optimization.
arXiv:2605. 18694v2 Announce Type: replace-cross Abstract: Many tasks in modern machine learning are observed to involve heavy-tailed gradient noise during the optimization process.