Operations research, mathematical programming, control theory.
Random-line Hessian estimates and a dyadic gradient tracker attain the minimax $\widetilde{\Theta}(\epsilon^{-3}+\gamma^{-5})$ oracle rate without the earlier mixed tolerance cost.
Verified recursive estimation and dense weak hiding yield matching higher-order oracle bounds with an $n^{1-1/(2p)}$ finite-sum term.
Adaptive access to $A$ and $A^\top$ yields matching polynomial query bounds for rank-$k$ projectors with $(1+\varepsilon)$-optimal Schatten-$p$ residuals.
Coordinate finite differences plus accelerated projection attain the deterministic rate, while a transcript-consistent hard instance proves it cannot generally be improved.
A large-step inexact Halpern wrapper accelerates tensor-based monotone variational-inequality solvers from polynomial rates up to a claimed near-$T^{-p}$ convergence rate.
A cone-preservation proof handles one fast and two identical slow servers, closing the first nontrivial case beyond Lin-Kumar’s two-server model.
Metric-compatible coarse corrections transfer gradients across manifolds, reducing iterations and CPU time on Kohn-Sham, Gross-Pitaevskii, and segmentation problems.
Post-processing Lagrangian dual certificates with sparsification and SDP searches cuts an FGM N=3 active set from 16 multipliers to 6.
Local trajectory contracts and safety envelopes let agents join or leave without central coordination, validated with up to eight race cars.
Random subspace methods achieve convergence rates dependent on intrinsic dimensionality, not ambient dimension.
