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Author: Documenter.jl

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+.DS_Store

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+.. _simple-example:
+
+Simple Example
+^^^^^^^^^^^^^^
+
+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::
+
+    using JuMP
+
+    m = Model()
+    @defVar(m, 0 <= x <= 2 )
+    @defVar(m, 0 <= y <= 30 )
+
+    @setObjective(m, Max, 5x + 3*y )
+    @addConstraint(m, 1x + 5y <= 3.0 )
+
+    print(m)
+
+    status = solve(m)
+
+    println("Objective value: ", getObjectiveValue(m))
+    println("x = ", getValue(x))
+    println("y = ", getValue(y))
+
+Once JuMP is :ref:`installed <jump-installation>`, to use JuMP in your
+programs, you just need to say::
+
+    using JuMP
+
+Models are created with the ``Model()`` function::
+
+    m = Model()
+
+.. note::
+   Your model doesn't have to be called m - it's just a name.
+
+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.::
+
+    @defVar(m, 0 <= x <= 2 )
+    @defVar(m, 0 <= y <= 30 )
+
+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``::
+
+    @setObjective(m, Max, 5x + 3*y )
+
+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 ``>=``::
+
+    @addConstraint(m, 1x + 5y <= 3.0 )
+
+If you want to see what your model looks like in a human-readable format,
+the ``print`` function is defined for models.
+
+::
+
+    print(m)
+
+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>`.
+
+::
+
+    status = solve(m)
+
+Finally, we can access the results of our optimization. Getting the objective
+value is simple::
+
+    println("Objective value: ", getObjectiveValue(m))
+
+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.
+
+::
+
+    println("x = ", getValue(x))
+    println("y = ", getValue(y))

0.12/_sources/callbacks.txt

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+===========================================
+JuMP --- Julia for Mathematical Programming
+===========================================
+
+.. module:: JuMP
+   :synopsis: Julia for Mathematical Programming
+
+`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:
+
+* 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 <http://www.ampl.com/>`_.
+  * 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 <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>`_.
+
+* Access to advanced algorithmic techniques
+
+  * 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.
+
+* 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 <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.
+
+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.
+
+Installing JuMP
+---------------
+
+If you are familiar with Julia you can get started quickly by using the
+package manager to install JuMP::
+
+    julia> Pkg.add("JuMP")
+
+And a solver, e.g.::
+
+    julia> Pkg.add("Clp")  # Will install Cbc as well
+
+Then read the :ref:`quick-start` and/or see a :ref:`simple-example`.
+The subsequent sections detail the complete functionality of JuMP.
+
+Contents
+--------
+
+.. toctree::
+    :maxdepth: 2
+
+    installation.rst
+    quickstart.rst
+    refmodel.rst
+    refvariable.rst
+    refexpr.rst
+    probmod.rst
+    callbacks.rst
+    nlp.rst
+
+-----------
+Citing JuMP
+-----------
+
+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>`_:
+
+.. code-block:: none
+
+    @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}
+    }
+
+A preprint of this paper is freely available on `arXiv <http://arxiv.org/abs/1312.1431>`_.
+
+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:
+
+.. code-block:: none
+
+    @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}
+    }