# JuMP: A Modeling Language for Mathematical Optimization

arXiv: https://arxiv.org/abs/1508.01982 · HTML: https://mlsanity.com/paper/1508.01982/

## Key facts

- Cited by 49 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Aug 2015.

## Built on by (most cited first, 30 of 49)

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- [Pushing the limits of fairness impossibility: Who's the fairest of them all?](https://mlsanity.com/paper/2208.12606/) (2022)
- [Data-Driven Sample Average Approximation with Covariate Information](https://mlsanity.com/paper/2207.13554/) (2022)
- [Confidence-Aware Graph Neural Networks for Learning Reliability Assessment Commitments](https://mlsanity.com/paper/2211.15755/) (2022)
- [Differentiation Through Black-Box Quadratic Programming Solvers](https://mlsanity.com/paper/2410.06324/) (2024)
- [Modeling Design and Control Problems Involving Neural Network Surrogates](https://mlsanity.com/paper/2111.10489/) (2021)
- [Motion Planning and Control for Multi Vehicle Autonomous Racing at High Speeds](https://mlsanity.com/paper/2207.11136/) (2022)
- [Slowly Varying Regression under Sparsity](https://mlsanity.com/paper/2102.10773/) (2021)
- [SeaPearl: A Constraint Programming Solver guided by Reinforcement Learning](https://mlsanity.com/paper/2102.09193/) (2021)
- [Learning Continuous Exponential Families Beyond Gaussian](https://mlsanity.com/paper/2102.09198/) (2021)
- [Sparse Bayesian Learning via Stepwise Regression](https://mlsanity.com/paper/2106.06095/) (2021)
- [Reachable Polyhedral Marching (RPM): An Exact Analysis Tool for Deep-Learned Control Systems](https://mlsanity.com/paper/2210.08339/) (2022)
- [PMLBmini: A Tabular Classification Benchmark Suite for Data-Scarce Applications](https://mlsanity.com/paper/2409.01635/) (2024)
- [Community Detection in the Stochastic Block Model by Mixed Integer Programming](https://mlsanity.com/paper/2101.12336/) (2021)
- [Advances in Trajectory Optimization for Space Vehicle Control](https://mlsanity.com/paper/2108.02335/) (2021)
- [Robust expected improvement for Bayesian optimization](https://mlsanity.com/paper/2302.08612/) (2023)
- [A Tutorial on the Design, Experimentation and Application of Metaheuristic Algorithms to Real-World Optimization Problems](https://mlsanity.com/paper/2410.03205/) (2024)
- [Chordal Sparsity for SDP-based Neural Network Verification](https://mlsanity.com/paper/2206.03482/) (2022)
- [A Physics-Informed Machine Learning for Electricity Markets: A NYISO Case Study](https://mlsanity.com/paper/2304.00062/) (2023)
- [A Neural Separation Algorithm for the Rounded Capacity Inequalities](https://mlsanity.com/paper/2306.17283/) (2023)
- [Data-driven decision-focused surrogate modeling](https://mlsanity.com/paper/2308.12161/) (2023)
- [Sparser, Better, Faster, Stronger: Sparsity Detection for Efficient Automatic Differentiation](https://mlsanity.com/paper/2501.17737/) (2025)
- [Convolutional Neural Nets in Chemical Engineering: Foundations, Computations, and Applications](https://mlsanity.com/paper/2101.04869/) (2021)
- [Efficient Learning of Decision-Making Models: A Penalty Block Coordinate Descent Algorithm for Data-Driven Inverse Optimization](https://mlsanity.com/paper/2210.15393/) (2022)
- [Cost-Sensitive Best Subset Selection for Logistic Regression: A Mixed-Integer Conic Optimization Perspective](https://mlsanity.com/paper/2310.05464/) (2023)
- [Randomized Forward Mode of Automatic Differentiation For Optimization Algorithms](https://mlsanity.com/paper/2310.14168/) (2023)

## Abstract (arXiv)

JuMP is an open-source modeling language that allows users to express a wide range of optimization problems (linear, mixed-integer, quadratic, conic-quadratic, semidefinite, and nonlinear) in a high-level, algebraic syntax. JuMP takes advantage of advanced features of the Julia programming language to offer unique functionality while achieving performance on par with commercial modeling tools for standard tasks. In this work we will provide benchmarks, present the novel aspects of the implementation, and discuss how JuMP can be extended to new problem classes and composed with state-of-the-art tools for visualization and interactivity.