# The ensmallen library for flexible numerical optimization

arXiv: https://arxiv.org/abs/2108.12981 · HTML: https://mlsanity.com/paper/2108.12981/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Aug 2021.

## Built on by (most cited first, 6 of 6)

- [SECA: Semantically Equivalent and Coherent Attacks for Eliciting LLM Hallucinations](https://mlsanity.com/paper/2510.04398/) (2025)
- [NCVX: A General-Purpose Optimization Solver for Constrained Machine and Deep Learning](https://mlsanity.com/paper/2210.00973/) (2022)
- [NCVX: A User-Friendly and Scalable Package for Nonconvex Optimization in Machine Learning](https://mlsanity.com/paper/2111.13984/) (2021)
- [Exact Reformulation and Optimization for Direct Metric Optimization in Binary Imbalanced Classification](https://mlsanity.com/paper/2507.15240/) (2025)
- [Solving Travelling Thief Problems using Coordination Based Methods](https://mlsanity.com/paper/2310.07156/) (2023)
- [Optimizing the Optimal Weighted Average: Efficient Distributed Sparse Classification](https://mlsanity.com/paper/2406.01753/) (2024)

## Abstract (arXiv)

We overview the ensmallen numerical optimization library, which provides a flexible C++ framework for mathematical optimization of user-supplied objective functions. Many types of objective functions are supported, including general, differentiable, separable, constrained, and categorical. A diverse set of pre-built optimizers is provided, including Quasi-Newton optimizers and many variants of Stochastic Gradient Descent. The underlying framework facilitates the implementation of new optimizers. Optimization of an objective function typically requires supplying only one or two C++ functions. Custom behavior can be easily specified via callback functions. Empirical comparisons show that ensmallen outperforms other frameworks while providing more functionality. The library is available at https://ensmallen.org and is distributed under the permissive BSD license.