# JuMP –- Julia for Mathematical Optimization

This documentation is for the development version of JuMP. JuMP is undergoing a major transition to MathOptInterface, and the documentation has not yet been rewritten. We **do not** recommend using the development version unless you are a JuMP or solver developer.

JuMP is a domain-specific modeling language for mathematical optimization embedded in Julia. It currently supports a number of open-source and commercial solvers (see below) for a variety of problem classes, including **linear programming**, **mixed-integer programming**, **second-order conic programming**, **semidefinite programming**, and **nonlinear programming**. JuMP's features include:

User friendliness

Syntax that mimics natural mathematical expressions.

Complete documentation.

Speed

Benchmarking has shown that JuMP can create problems at similar speeds to special-purpose modeling languages such as AMPL.

JuMP communicates with solvers in memory, avoiding the need to write intermediary files.

Solver independence

JuMP uses a generic solver-independent interface provided by the MathProgBase package, making it easy to change between a number of open-source and commercial optimization software packages ("solvers").

Currently supported solvers include Artelys Knitro, Bonmin, Cbc, Clp, Couenne, CPLEX, ECOS, FICO Xpress, GLPK, Gurobi, Ipopt, MOSEK, NLopt, and SCS.

Access to advanced algorithmic techniques

Including efficient LP re-solves which previously required using solver-specific and/or low-level C++ libraries.

Ease of embedding

JuMP itself is written purely in Julia. Solvers are the only binary dependencies.

Being embedded in a general-purpose programming language makes it easy to solve optimization problems as part of a larger workflow (e.g., inside a simulation, behind a web server, or as a subproblem in a decomposition algorithm).

As a trade-off, JuMP's syntax is constrained by the syntax available in Julia.

JuMP is MPL licensed, meaning that it can be embedded in commercial software that complies with the terms of the license.

While neither Julia nor JuMP have reached version 1.0 yet, the releases are stable enough for everyday use and are being used in a number of research projects and neat applications by a growing community of users who are early adopters. JuMP remains under active development, and we welcome your feedback, suggestions, and bug reports.

## Contents

- Installation Guide
- Quick Start Guide
- Expressions and Constraints
- Problem Modification
- Nonlinear Modeling

### Citing JuMP

If you find JuMP useful in your work, we kindly request that you cite the following paper (pdf):

```
@article{DunningHuchetteLubin2017,
author = {Iain Dunning and Joey Huchette and Miles Lubin},
title = {JuMP: A Modeling Language for Mathematical Optimization},
journal = {SIAM Review},
volume = {59},
number = {2},
pages = {295-320},
year = {2017},
doi = {10.1137/15M1020575},
}
```

For an earlier work where we presented a prototype implementation of JuMP, see here:

```
@article{LubinDunningIJOC,
author = {Miles Lubin and Iain Dunning},
title = {Computing in Operations Research Using Julia},
journal = {INFORMS Journal on Computing},
volume = {27},
number = {2},
pages = {238-248},
year = {2015},
doi = {10.1287/ijoc.2014.0623},
}
```

A preprint of this paper is freely available.