# A first-order multigrid method for bound-constrained convex optimization

arXiv: https://arxiv.org/abs/1602.03771 · HTML: https://mlsanity.com/paper/1602.03771/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2016.

## Built on by (most cited first, 2 of 2)

- [Recursive Bound-Constrained AdaGrad with Applications to Multilevel and Domain Decomposition Minimization](https://mlsanity.com/paper/2507.11513/) (2025)
- [Multilevel Geometric Optimization for Regularised Constrained Linear Inverse Problems](https://mlsanity.com/paper/2207.04934/) (2022)

## Abstract (arXiv)

The aim of this paper is to design an efficient multigrid method for constrained convex optimization problems arising from discretization of some underlying infinite dimensional problems. Due to problem dependency of this approach, we only consider bound constraints with (possibly) a single equality constraint. As our aim is to target large-scale problems, we want to avoid computation of second derivatives of the objective function, thus excluding Newton like methods. We propose a smoothing operator that only uses first-order information and study the computational efficiency of the resulting method.