# Complexity of Adagrad and other first-order methods for nonconvex optimization problems with bounds constraints

arXiv: https://arxiv.org/abs/2406.15793 · HTML: https://mlsanity.com/paper/2406.15793/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jun 2024.

## Built on by (most cited first, 1 of 1)

- [Recursive Bound-Constrained AdaGrad with Applications to Multilevel and Domain Decomposition Minimization](https://mlsanity.com/paper/2507.11513/) (2025)

## Abstract (arXiv)

A parametric class of trust-region algorithms for constrained nonconvex optimization is analyzed, where the objective function is never computed. By defining appropriate first-order stationarity criteria, we are able to extend the Adagrad method to the newly considered problem and retrieve the standard complexity rate of the projected gradient method that uses both the gradient and objective function values. Furthermore, we propose an additional iteration-dependent scaling with slightly inferior theoretical guarantees. In both cases, the bounds are essentially sharp, and curvature information can be used to compute the stepsize. Initial experimental results for noisy bound-constrained instances illustrate the benefits of the objective-free approach.