This documentation is for the development branch of JuMP. JuMP is undergoing a major transition to MathOptInterface. The development version is beta quality and the documentation has TODOs remaining before the release. Please provide feedback and file issues if you use this branch.

The NEWS.md file contains a comprehensive list of the changes between JuMP 0.18 and JuMP 0.19 to aid users updating their existing models.

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 (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").
- 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.

Although JuMP has not 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
- Variables
- What is a JuMP variable?
- Variable bounds
- Variable names
- Variable containers
- Integrality shortcuts
- Semidefinite variables
- Anonymous JuMP variables
- User-defined containers
- Deleting variables
- Listing all variables
- Reference
- Expressions
- Objective
- Constraints
- The
`@constraint`

macro - Duality
- Constraint names
- Constraint containers
- Vectorized constraints
- Constraints on a single variable
- Constraints on a collection of variables
- Quadratic constraints
- Semidefinite constraints
- Constraint modifications
- Constraint deletion
- Function-Set pairs
- Reference
- Constructing constraints without adding them to the model
- Containers
- Interacting with solvers
- Querying Solutions
- Nonlinear Modeling
- Syntax notes
- Nonlinear Parameters
- User-defined Functions
- Factors affecting solution time
- Querying derivatives from a JuMP model
- Raw expression input
- Reference
- Style guide and design principles
- Extending JuMP

### 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.

JuMP is a fiscally sponsored project of NumFOCUS, a nonprofit dedicated to supporting the open source scientific computing community.

You can support JuMP by donating. 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.