# MathOptInterface: a data structure for mathematical optimization problems

arXiv: https://arxiv.org/abs/2002.03447 · HTML: https://mlsanity.com/paper/2002.03447/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Feb 2020.

## Built on by (most cited first, 9 of 9)

- [Flexible Differentiable Optimization via Model Transformations](https://mlsanity.com/paper/2206.06135/) (2022)
- [Synthesis of Mathematical programs from Natural Language Specifications](https://mlsanity.com/paper/2304.03287/) (2023)
- [SeaPearl: A Constraint Programming Solver guided by Reinforcement Learning](https://mlsanity.com/paper/2102.09193/) (2021)
- [Convex mixed-integer optimization with Frank-Wolfe methods](https://mlsanity.com/paper/2208.11010/) (2022)
- [Stabilizing reinforcement learning control: A modular framework for optimizing over all stable behavior](https://mlsanity.com/paper/2310.14098/) (2023)
- [AbstractDifferentiation.jl: Backend-Agnostic Differentiable Programming in Julia](https://mlsanity.com/paper/2109.12449/) (2021)
- [MathOptAI.jl: Embed trained machine learning predictors into JuMP models](https://mlsanity.com/paper/2507.03159/) (2025)
- [FLARE: Verifying MILP Reformulations with LLM-Based Theorem Proving](https://mlsanity.com/paper/2608.25220/) (2026)
- [TorchDCM: A Unified PyTorch-Native Package for Discrete Choice Modeling](https://mlsanity.com/paper/2608.19231/) (2026)

## Abstract (arXiv)

We introduce MathOptInterface, an abstract data structure for representing mathematical optimization problems based on combining pre-defined functions and sets. MathOptInterface is significantly more general than existing data structures in the literature, encompassing, for example, a spectrum of problems classes from integer programming with indicator constraints to bilinear semidefinite programming. We also outline an automated rewriting system between equivalent formulations of a constraint. MathOptInterface has been implemented in practice, forming the foundation of a recent rewrite of JuMP, an open-source algebraic modeling language in the Julia language. The regularity of the MathOptInterface representation leads naturally to a general file format for mathematical optimization we call MathOptFormat. In addition, the automated rewriting system provides modeling power to users while making it easy to connect new solvers to JuMP.