MathOptInterface: a data structure for mathematical optimization problems
Abstract
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.
Cite
@article{arxiv.2002.03447,
title = {MathOptInterface: a data structure for mathematical optimization problems},
author = {Benoit Legat and Oscar Dowson and Joaquim Dias Garcia and Miles Lubin},
journal= {arXiv preprint arXiv:2002.03447},
year = {2026}
}