Papers › A consistently adaptive trust-region method
A consistently adaptive trust-region method
Fadi Hamad, Oliver Hinder
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
Adaptive trust-region methods attempt to maintain strong convergence guarantees without depending on conservative estimates of problem properties such as Lipschitz constants. However, on close inspection, one can show existing adaptive trust-region methods have theoretical guarantees with severely suboptimal dependence on problem properties such as the Lipschitz constant of the Hessian. For example, TRACE developed by Curtis et al. obtains a O(Δ_f L^(3/2) ϵ^(-3/2)) + Õ(1) iteration bound where L is the Lipschitz constant of the Hessian. Compared with the optimal O(Δ_f L^(1/2) ϵ^(-3/2)) bound this is suboptimal with respect to L. We present the first adaptive trust-region method which circumvents this issue and requires at most O( Δ_f L^(1/2) ϵ^(-3/2)) + Õ(1) iterations to find an ϵ-approximate stationary point, matching the optimal iteration bound up to an additive logarithmic term. Our method is a simple variant of a classic trust-region method and in our experiments performs competitively with both ARC and a classical trust-region method.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections