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.. _simple-example: | ||
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Simple Example | ||
^^^^^^^^^^^^^^ | ||
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In this section we will construct a simple model and explain every step along the way. | ||
The are more complex examples in the ``JuMP/examples/`` `folder <https://github.com/JuliaOpt/JuMP.jl/tree/master/examples>`_. Here is the code we will walk through:: | ||
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using JuMP | ||
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m = Model() | ||
@defVar(m, 0 <= x <= 2 ) | ||
@defVar(m, 0 <= y <= 30 ) | ||
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@setObjective(m, Max, 5x + 3*y ) | ||
@addConstraint(m, 1x + 5y <= 3.0 ) | ||
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print(m) | ||
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status = solve(m) | ||
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println("Objective value: ", getObjectiveValue(m)) | ||
println("x = ", getValue(x)) | ||
println("y = ", getValue(y)) | ||
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Once JuMP is :ref:`installed <jump-installation>`, to use JuMP in your | ||
programs, you just need to say:: | ||
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using JuMP | ||
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Models are created with the ``Model()`` function:: | ||
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m = Model() | ||
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.. note:: | ||
Your model doesn't have to be called m - it's just a name. | ||
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There are a few options for defining a variable, depending on whether you want | ||
to have lower bounds, upper bounds, both bounds, or even no bounds. The following | ||
commands will create two variables, ``x`` and ``y``, with both lower and upper bounds. | ||
Note the first argument is our model variable ``m``. These variables are associated | ||
with this model and cannot be used in another model.:: | ||
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@defVar(m, 0 <= x <= 2 ) | ||
@defVar(m, 0 <= y <= 30 ) | ||
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Next we'll set our objective. Note again the ``m``, so we know which model's | ||
objective we are setting! The objective sense, ``Max`` or ``Min``, should | ||
be provided as the second argument. Note also that we don't have a multiplication ``*`` | ||
symbol between 5 and our variable ``x`` - Julia is smart enough to not need it! | ||
Feel free to stick with ``*`` if it makes you feel more comfortable, as we have | ||
done with ``3*y``:: | ||
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@setObjective(m, Max, 5x + 3*y ) | ||
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Adding constraints is a lot like setting the objective. Here we create a | ||
less-than-or-equal-to constraint using ``<=``, but we can also create equality | ||
constraints using ``==`` and greater-than-or-equal-to constraints with ``>=``:: | ||
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@addConstraint(m, 1x + 5y <= 3.0 ) | ||
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If you want to see what your model looks like in a human-readable format, | ||
the ``print`` function is defined for models. | ||
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:: | ||
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print(m) | ||
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Models are solved with the ``solve()`` function. This function will not raise | ||
an error if your model is infeasible - instead it will return a flag. In this | ||
case, the model is feasible so the value of ``status`` will be ``:Optimal``, | ||
where ``:`` again denotes a symbol. The possible values of ``status`` | ||
are described :ref:`here <solvestatus>`. | ||
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:: | ||
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status = solve(m) | ||
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Finally, we can access the results of our optimization. Getting the objective | ||
value is simple:: | ||
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println("Objective value: ", getObjectiveValue(m)) | ||
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To get the value from a variable, we call the ``getValue()`` function. If ``x`` | ||
is not a single variable, but instead a range of variables, ``getValue()`` will | ||
return a list. In this case, however, it will just return a single value. | ||
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:: | ||
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println("x = ", getValue(x)) | ||
println("y = ", getValue(y)) |
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=========================================== | ||
JuMP --- Julia for Mathematical Programming | ||
=========================================== | ||
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.. module:: JuMP | ||
:synopsis: Julia for Mathematical Programming | ||
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`JuMP <https://github.com/JuliaOpt/JuMP.jl>`_ is a domain-specific modeling language for | ||
`mathematical programming <http://en.wikipedia.org/wiki/Mathematical_optimization>`_ | ||
embedded in `Julia <http://julialang.org/>`_. | ||
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: | ||
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* User friendliness | ||
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* Syntax that mimics natural mathematical expressions. | ||
* Complete documentation. | ||
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* Speed | ||
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* Benchmarking has shown that JuMP can create problems at similar speeds to | ||
special-purpose modeling languages such as `AMPL <http://www.ampl.com/>`_. | ||
* JuMP communicates with solvers in memory, avoiding the need to write | ||
intermediary files. | ||
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* Solver independence | ||
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* JuMP uses a generic solver-independent interface provided by the | ||
`MathProgBase <https://github.com/mlubin/MathProgBase.jl>`_ package, making it easy | ||
to change between a number of open-source and commercial optimization software packages ("solvers"). | ||
* Currently supported solvers include | ||
`Bonmin <https://projects.coin-or.org/Bonmin>`_, | ||
`Cbc <https://projects.coin-or.org/Cbc>`_, | ||
`Clp <https://projects.coin-or.org/Clp>`_, | ||
`Couenne <https://projects.coin-or.org/Couenne>`_, | ||
`CPLEX <http://www-01.ibm.com/software/commerce/optimization/cplex-optimizer/>`_, | ||
`ECOS <https://github.com/ifa-ethz/ecos>`_, | ||
`GLPK <http://www.gnu.org/software/glpk/>`_, | ||
`Gurobi <http://www.gurobi.com>`_, | ||
`Ipopt <https://projects.coin-or.org/Ipopt>`_, | ||
`KNITRO <http://www.ziena.com/knitro.htm>`_, | ||
`MOSEK <http://www.mosek.com/>`_, | ||
`NLopt <http://ab-initio.mit.edu/wiki/index.php/NLopt>`_, | ||
and `SCS <https://github.com/cvxgrp/scs>`_. | ||
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* Access to advanced algorithmic techniques | ||
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* Including :ref:`efficient LP re-solves <probmod>` and :ref:`callbacks for mixed-integer programming <callbacks>` which previously required using solver-specific and/or low-level C++ libraries. | ||
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* Ease of embedding | ||
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* 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). | ||
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* As a trade-off, JuMP's syntax is constrained by the syntax available in Julia. | ||
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* JuMP is `MPL <https://www.mozilla.org/MPL/2.0/>`_ licensed, meaning that it can be embedded in commercial software that complies with the terms of the license. | ||
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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. | ||
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Installing JuMP | ||
--------------- | ||
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If you are familiar with Julia you can get started quickly by using the | ||
package manager to install JuMP:: | ||
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julia> Pkg.add("JuMP") | ||
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And a solver, e.g.:: | ||
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julia> Pkg.add("Clp") # Will install Cbc as well | ||
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Then read the :ref:`quick-start` and/or see a :ref:`simple-example`. | ||
The subsequent sections detail the complete functionality of JuMP. | ||
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Contents | ||
-------- | ||
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.. toctree:: | ||
:maxdepth: 2 | ||
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installation.rst | ||
quickstart.rst | ||
refmodel.rst | ||
refvariable.rst | ||
refexpr.rst | ||
probmod.rst | ||
callbacks.rst | ||
nlp.rst | ||
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----------- | ||
Citing JuMP | ||
----------- | ||
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If you find JuMP useful in your work, we kindly request that you cite the following `paper <http://dx.doi.org/10.1287/ijoc.2014.0623>`_: | ||
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.. code-block:: none | ||
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@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}, | ||
URL = {http://dx.doi.org/10.1287/ijoc.2014.0623} | ||
} | ||
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A preprint of this paper is freely available on `arXiv <http://arxiv.org/abs/1312.1431>`_. | ||
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If you use the nonlinear or conic optimization functionality of JuMP, please cite the following `preprint <http://arxiv.org/abs/1508.01982>`_ which describes the methods implemented in JuMP. You may cite it as: | ||
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.. code-block:: none | ||
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@article{DunningHuchetteLubin2015, | ||
title = {{JuMP}: {A} modeling language for mathematical optimization}, | ||
author = {Iain Dunning and Joey Huchette and Miles Lubin}, | ||
journal = {arXiv:1508.01982 [math.OC]}, | ||
year = {2015}, | ||
url = {http://arxiv.org/abs/1508.01982} | ||
} |
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