# A note on solving nonlinear optimization problems in variable precision

arXiv: https://arxiv.org/abs/1812.03467 · HTML: https://mlsanity.com/paper/1812.03467/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Dec 2018.

## 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)
- [Efficient Constant Optimization for Symbolic Regression with GPU-Accelerated Tree-Based Genetic Programming](https://mlsanity.com/paper/2609.03352/) (2026)

## Abstract (arXiv)

This short note considers an efficient variant of the trust-region algorithm with dynamic accuracy proposed Carter (1993) and Conn, Gould and Toint (2000) as a tool for very high-performance computing, an area where it is critical to allow multi-precision computations for keeping the energy dissipation under control. Numerical experiments are presented indicating that the use of the considered method can bring substantial savings in objective function's and gradient's evaluation "energy costs" by efficiently exploiting multi-precision computations.