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Warning

Between versions 0.18 and 0.19, JuMP underwent a major transition in its underlying solver abstraction API, from MathProgBase to MathOptInterface. See NEWS.md for a comprehensive list of changes between the two versions, many of which are breaking. This documentation is for JuMP/MathOptInterface. For the documentation of JuMP 0.18, see here.

What is JuMP?

JuMP is a domain-specific modeling language for mathematical optimization embedded in Julia. It currently supports a number of open-source and commercial solvers for a variety of problem classes, including linear, mixed-integer, second-order conic, semidefinite, and nonlinear programming.

Resources for getting started

Key features

JuMP's features include:

  • User friendliness
    • Syntax that mimics natural mathematical expressions.
    • Complete documentation (WIP!)
  • Speed
    • Benchmarking has shown that JuMP can create problems at similar speeds to special-purpose modeling languages such as AMPL.
    • JuMP communicates with most solvers in memory, avoiding the need to write intermediary files.
  • Solver independence
    • JuMP uses a generic solver-independent interface provided by the MathOptInterface package, making it easy to change between a number of open-source and commercial optimization software packages ("solvers"). The Supported solvers section contains a table of the currently supported solvers.
  • 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.

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.


NumFOCUS logo

JuMP is a Sponsored Project of NumFOCUS, a 501(c)(3) nonprofit charity in the United States. NumFOCUS provides JuMP with fiscal, legal, and administrative support to help ensure the health and sustainability of the project. Visit numfocus.org for more information.

You can support JuMP by donating.

Donations to JuMP are managed by NumFOCUS. For donors in the United States, your gift is tax-deductible to the extent provided by law. As with any donation, you should consult with your tax adviser about your particular tax situation.

JuMP's largest expense is the annual JuMP-dev workshop. Donations will help us provide travel support for JuMP-dev attendees and take advantage of other opportunities that arise to support JuMP development.