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<!DOCTYPE html>
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<meta name="description" content="JuliaOpt - Optimization packages for the Julia language">
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HELLO
<div class="container">
<!-- Big box at top -->
<div class="jumbotron text-center">
<img style="height: 12em; width:auto" src="/images/juliaopt.svg">
<h1>JuliaOpt</h1>
<p>
Optimization packages for the <a href="http://julialang.org">Julia language.</a>
</p>
</div>
<hr>
<!--<div class="row">
<div class="col-md-12 text-center">
<h2>JuliaOpt at <a href="http://juliacon.org">JuliaCon 2015</a></h2>
<p>
There will be a JuliaOpt talk and three-hour workshop at JuliaCon 2015, held at MIT in Cambridge, Massachusetts from June 24th-28th. <a href="http://www.eventbrite.com/e/juliacon-2015-tickets-16517619645">Tickets are on sale now!</a>.
</p>
</div>
</div>
<hr>-->
<!-- Julia & JuliaOpt-->
<a id="about"></a>
<div class="row">
<div class="col-md-6">
<h1>What is Julia?</h1>
<p>
<a href="http://julialang.org">"Julia is a high-level, high-performance dynamic programming language for technical computing"</a>. It is free (open source) and supports Windows, OSX, and Linux. It has a familiar syntax, works well with external libraries, is fast, and has advanced language features like metaprogramming that enable interesting possibilities for optimization software.
</p>
<p>
<b>Case study</b>: <a href="http://dx.doi.org/10.1287/ijoc.2014.0623">"Computing in Operations Research using Julia"</a>. <i>INFORMS Journal on Computing</i>. <a href="http://arxiv.org/abs/1312.1431">[PDF]</a>.
</p>
</div>
<div class="col-md-6">
<h1>What is JuliaOpt?</h1>
<p>
JuliaOpt is an organization that brings together packages written in Julia that are related to optimization. All JuliaOpt packages should be high-quality, documented, tested, support the main operating systems, and interact with each other.
<ul>
<li><b>Overview</b>: <a href="https://www.youtube.com/watch?v=7LNeR299q88">presentation</a> and <a href="https://www.youtube.com/watch?v=nnL7yLMVu6c">workshop</a> from JuliaCon 2015</a></li>
<li><b>Code</b>: <a href="http://github.com/JuliaOpt">github.com/JuliaOpt</a></li>
<li><b>Mailing list</b>: <a href="https://groups.google.com/forum/#!forum/julia-opt">julia-opt</a></li>
</ul>
</p>
</div>
</div>
<div class="row">
<div class="col-md-6">
<h2>Getting Started</h2>
<ol>
<li>
You can find <a href="http://julialang.org/downloads/">downloads and installation instructions for Julia</a> for your operating system on the Julia site.
</li>
<li>
To install a JuliaOpt package, simply use the <code>Pkg.add</code> command from inside Julia:<br>
<code>
julia> Pkg.update() # Get latest package info<br>
julia> Pkg.add("Optim")<br>
julia> Pkg.add("JuMP")<br>
julia> Pkg.add("Cbc") # and so on
</code>
</li>
<li>
<b>Open-source</b> solvers will automatically be downloaded and installed in your Julia package directory. If you want to use an external <b>commercial</b> solver, you will need to download those before installing the corresponding JuliaOpt package.
</li>
</ol>
</div>
<div class="col-md-6">
<h2>Examples</h2>
<div class="text-center" style="margin-bottom: 10px">
<img style="height: 4em; width:auto" src="/images/ijulialogo.png">
</div>
<p>
We have a collection of JuliaOpt examples in the form of <a href="https://jupyter.org/">Jupyter</a>/<a href="https://github.com/JuliaLang/IJulia.jl">IJulia</a> notebooks, including:
<ul>
<li><a href="/notebooks/JuMP-Sudoku.html">Solving Sudoku puzzles with JuMP</a>,
<li><a href="/notebooks/JuMP-Rocket.html">Controlling a rocket with JuMP</a>,
<li>and <a href="/notebooks/index.html">many more</a>.
</ul>
The source for these notebooks is <a href="https://github.com/JuliaOpt/juliaopt-notebooks">available here</a>.
</p>
</div>
</div>
<a id="packages"></a>
<div class="row">
<div class="col-md-12">
<h1>Overview of Packages</h1>
<p>JuliaOpt's packages can be loosely grouped into two sets. The first set are standalone Julia packages:</p>
<ul>
<li>
<strong>Optim.jl</strong>
- Implementations in Julia of standard optimization algorithms for unconstrained or box-constrained problems such as BFGS, Nelder-Mead, conjugate gradient, etc.
(<a href="https://github.com/JuliaOpt/Optim.jl">documentation/code</a>)
</li>
<li>
<strong>LsqFit.jl</strong>
- Least-squares non-linear curve fitting in Julia.
(<a href="https://github.com/JuliaOpt/LsqFit.jl">documentation/code</a>)
</li>
</ul>
<p>The second set comprises modeling languages (red), external solver interfaces (purple), and an abstraction layer over the solvers (green), primarily for constrained optimization:
<ul>
<li>
<strong>JuMP</strong>
- An algebraic modeling language for linear, quadratic, and nonlinear constrained optimization problems embedded in Julia. Generates models as quick as commercial modeling tools and supports advanced features like solver callbacks. (<a href="https://jump.readthedocs.org/en/latest/">documentation</a>, <a href="https://github.com/JuliaOpt/JuMP.jl">code</a>)
</li>
<li>
<strong>Convex.jl</strong>
- An algebraic modeling language for <a href="http://stanford.edu/~boyd/papers/disc_cvx_prog.html">disciplined convex programming</a> embedded in Julia.
(<a href="http://convexjl.readthedocs.org/">documentation</a>, <a href="https://github.com/JuliaOpt/Convex.jl">code</a>)
</li>
<li><strong>MathProgBase</strong> - A standardized interface implemented by all solvers that allows code to remain solver-agnostic. Used by JuMP and Convex.jl, but can be called by user code directly if a user doesn't want to go through a modeling language, but wishes to remain solver-independent. (<a href="http://mathprogbasejl.readthedocs.org/en/latest/">documentation</a>, <a href="https://github.com/JuliaOpt/MathProgBase.jl">code</a>)</li>
</ul>
<p>
JuliaOpt provides wrappers for a wide variety of solvers. The following table summarizes the capabilities of each solver, and also shows the problem forms supported by the two modeling languages.
</p>
<table style="text-align: center; margin-top: 20px" width="100%">
<thead>
<tr>
<th width="23%"><strong>Modeling Tool</strong></th>
<th width="9%">LP</th>
<th width="9%">MILP</th>
<th width="9%">SOCP</th>
<th width="9%">MISOCP</th>
<th width="9%">SDP</th>
<th width="9%">NLP</th>
<th width="9%">MINLP</th>
<th>Other</th>
</tr>
</thead>
<tfoot> <!-- Must appear before tbody, see W3.org -->
<tr style="text-align: left">
<td colspan="10">
<small>
<strong>Key:</strong>
<ul style="list-style: none; margin-top: 5px; margin-bottom: 5px">
<li style="margin: 0.1em 0;">LP = <a href="http://en.wikipedia.org/wiki/Linear_programming">Linear Programming</a></li>
<li style="margin: 0.1em 0;">MILP = <a href="http://en.wikipedia.org/wiki/Integer_programming">Mixed Integer LP</a></li>
<li style="margin: 0.1em 0;">SOCP = <a href="http://en.wikipedia.org/wiki/Second_order_cone_programming">Second-order cone programming</a> (includes convex <a href="http://en.wikipedia.org/wiki/Quadratic_programming">QP</a>, <a href="http://en.wikipedia.org/wiki/Quadratically_constrained_quadratic_program">QCQP</a>)</li>
<li style="margin: 0.1em 0;">MISOCP = Mixed Integer SOCP</li>
<li style="margin: 0.1em 0;">SDP = <a href="http://en.wikipedia.org/wiki/Semidefinite_programming">Semidefinite Programming</a></li>
<li style="margin: 0.1em 0;">NLP = (constrained) <a href="http://en.wikipedia.org/wiki/Nonlinear_programming">Nonlinear Programming</a> (includes general <a href="http://en.wikipedia.org/wiki/Quadratic_programming">QP</a>, <a href="http://en.wikipedia.org/wiki/Quadratically_constrained_quadratic_program">QCQP</a>)</li>
<li style="margin: 0.1em 0;">MINLP = Mixed Integer NLP</li>
</ul>
<strong>Notes:</strong>
<ol style="">
<li>Problem must be convex.</li>
</ol>
</small>
</td>
</tr>
</tfoot>
<tbody>
<tr>
<th><a href="https://github.com/JuliaOpt/JuMP.jl">JuMP</a></th>
<td>✔</td> <!-- LP -->
<td>✔</td> <!-- MILP -->
<td>✔</td> <!-- SOCP -->
<td>✔</td> <!-- MISOCP -->
<td>✔</td> <!-- SDP -->
<td>✔</td> <!-- NLP -->
<td>✔</td> <!-- MINLP -->
<td></td> <!-- Other -->
</tr>
<tr>
<th><a href="https://github.com/cvxgrp/Convex.jl">Convex.jl</a></th>
<td>✔</td> <!-- LP -->
<td>✔</td> <!-- MILP -->
<td>✔</td> <!-- SOCP -->
<td>✔</td> <!-- MISOCP -->
<td>✔</td> <!-- SDP -->
<td></td> <!-- NLP -->
<td></td> <!-- MINLP -->
<td></td> <!-- Other -->
</tr>
<thead>
<tr>
<th><strong>Solver</strong></th>
<th>LP</th>
<th>MILP</th>
<th>SOCP</th>
<th>MISOCP</th>
<th>SDP</th>
<th>NLP</th>
<th>MINLP</th>
<th>Other</th>
</tr>
</thead>
<tr>
<th>
<a href="https://projects.coin-or.org/Bonmin">Bonmin</a>
<a href="https://github.com/JuliaOpt/AmplNLWriter.jl">(via AmplNLWriter.jl)</a>
</th>
<td>✔</td> <!-- LP -->
<td>✔</td> <!-- MILP -->
<td></td> <!-- SOCP -->
<td></td> <!-- MISOCP -->
<td></td> <!-- SDP -->
<td>✔</td> <!-- NLP -->
<td>✔</td> <!-- MINLP -->
<td></td> <!-- Other -->
</tr>
<tr>
<th>
<a href="https://projects.coin-or.org/Cbc">Cbc</a>
<a href="https://github.com/JuliaOpt/Cbc.jl">(.jl)</a>
</th>
<td>✔</td> <!-- LP -->
<td>✔</td> <!-- MILP -->
<td></td> <!-- SOCP -->
<td></td> <!-- MISOCP -->
<td></td> <!-- SDP -->
<td></td> <!-- NLP -->
<td></td> <!-- MINLP -->
<td></td> <!-- Other -->
</tr>
<tr>
<th>
<a href="https://projects.coin-or.org/Clp">Clp</a>
<a href="https://github.com/JuliaOpt/Clp.jl">(.jl)</a>
</th>
<td>✔</td> <!-- LP -->
<td></td> <!-- MILP -->
<td></td> <!-- SOCP -->
<td></td> <!-- MISOCP -->
<td></td> <!-- SDP -->
<td></td> <!-- NLP -->
<td></td> <!-- MINLP -->
<td></td> <!-- Other -->
</tr>
<tr>
<th>
<a href="https://projects.coin-or.org/Couenne">Couenne</a>
<a href="https://github.com/JuliaOpt/AmplNLWriter.jl">(via AmplNLWriter.jl)</a>
</th>
<td>✔</td> <!-- LP -->
<td>✔</td> <!-- MILP -->
<td></td> <!-- SOCP -->
<td></td> <!-- MISOCP -->
<td></td> <!-- SDP -->
<td>✔</td> <!-- NLP -->
<td>✔</td> <!-- MINLP -->
<td></td> <!-- Other -->
</tr>
<tr>
<th>
<a href="http://www-01.ibm.com/software/commerce/optimization/cplex-optimizer/">CPLEX</a>
<a href="https://github.com/JuliaOpt/CPLEX.jl">(.jl)</a>
</th>
<!--<td><a href="https://github.com/JuliaOpt/CPLEX.jl">CPLEX.jl</a></td>-->
<td>✔</td> <!-- LP -->
<td>✔</td> <!-- MILP -->
<td>✔</td> <!-- SOCP -->
<td>✔</td> <!-- MISOCP -->
<td></td> <!-- SDP -->
<td></td> <!-- NLP -->
<td></td> <!-- MINLP -->
<td><small>IP Callbacks</small></td> <!-- Other -->
</tr>
<tr>
<th>
<a href="https://github.com/ifa-ethz/ecos/">ECOS</a>
<a href="https://github.com/JuliaOpt/ECOS.jl">(.jl)</a>
</th>
<!--<td><a href="https://github.com/JuliaOpt/ECOS.jl">ECOS.jl</a></td>-->
<td>✔</td> <!-- LP -->
<td></td> <!-- MILP -->
<td>✔</td> <!-- SOCP -->
<td></td> <!-- MISOCP -->
<td></td> <!-- SDP -->
<td></td> <!-- NLP -->
<td></td> <!-- MINLP -->
<td></td> <!-- Other -->
</tr>
<tr>
<th>
<a href="http://www.gnu.org/software/glpk/">GLPK</a>
<a href="https://github.com/JuliaOpt/GLPK.jl">(.jl)</a>
</th>
<!--<td><a href="https://github.com/JuliaOpt/GLPK.jl">GLPK.jl</a></td>-->
<td>✔</td> <!-- LP -->
<td>✔</td> <!-- MILP -->
<td></td> <!-- SOCP -->
<td></td> <!-- MISOCP -->
<td></td> <!-- SDP -->
<td></td> <!-- NLP -->
<td></td> <!-- MINLP -->
<td><small>IP Callbacks</small></td> <!-- Other -->
</tr>
<tr>
<th>
<a href="http://www.gurobi.com">Gurobi</a>
<a href="https://github.com/JuliaOpt/Gurobi.jl">(.jl)</a>
</th>
<!--<td><a href="https://github.com/JuliaOpt/Gurobi.jl">Gurobi.jl</a></td>-->
<td>✔</td> <!-- LP -->
<td>✔</td> <!-- MILP -->
<td>✔</td> <!-- SOCP -->
<td>✔</td> <!-- MISOCP -->
<td></td> <!-- SDP -->
<td></td> <!-- NLP -->
<td></td> <!-- MINLP -->
<td><small>IP Callbacks</small></td> <!-- Other -->
</tr>
<tr>
<th>
<a href="https://projects.coin-or.org/Ipopt">Ipopt</a>
<a href="https://github.com/JuliaOpt/Ipopt.jl">(.jl)</a>
</th>
<!--<td><a href="https://github.com/JuliaOpt/Ipopt.jl">Ipopt.jl</a></td>-->
<td>✔</td> <!-- LP -->
<td></td> <!-- MILP -->
<td></td> <!-- SOCP -->
<td></td> <!-- MISOCP -->
<td></td> <!-- SDP -->
<td>✔</td> <!-- NLP -->
<td></td> <!-- MINLP -->
<td></td> <!-- Other -->
</tr>
<tr>
<th>
<a href="http://artelys.com/en/optimization-tools/knitro">Artelys Knitro</a>
<a href="https://github.com/JuliaOpt/KNITRO.jl">(.jl)</a>
</th>
<!--<td><a href="https://github.com/JuliaOpt/KNITRO.jl/">KNITRO.jl</a></td>-->
<td>✔</td> <!-- LP -->
<td>✔</td></td> <!-- MILP -->
<td></td> <!-- SOCP -->
<td></td> <!-- MISOCP -->
<td></td> <!-- SDP -->
<td>✔</td> <!-- NLP -->
<td>✔</td></td> <!-- MINLP -->
<td></td> <!-- Other -->
</tr>
<tr>
<th>
<a href="http://www.mosek.com/">Mosek</a>
<a href="https://github.com/JuliaOpt/Mosek.jl">(.jl)</a>
</th>
<!--<td><a href="https://github.com/JuliaOpt/Mosek.jl">Mosek.jl</a></td>-->
<td>✔</td> <!-- LP -->
<td>✔</td> <!-- MILP -->
<td>✔</td> <!-- SOCP -->
<td>✔</td> <!-- MISOCP -->
<td>✔</td> <!-- SDP -->
<td>✔<small>1</small></td> <!-- NLP -->
<td></td> <!-- MINLP -->
<td></td> <!-- Other -->
</tr>
<tr>
<th>
<a href="http://ab-initio.mit.edu/nlopt">NLopt</a>
<a href="https://github.com/JuliaOpt/NLopt.jl">(.jl)</a>
</th>
<!--<td><a href="https://github.com/JuliaOpt/NLopt.jl">NLopt.jl</a></td>-->
<td></td> <!-- LP -->
<td></td> <!-- MILP -->
<td></td> <!-- SOCP -->
<td></td> <!-- MISOCP -->
<td></td> <!-- SDP -->
<td>✔</td> <!-- NLP -->
<td></td> <!-- MINLP -->
<td></td> <!-- Other -->
</tr>
<tr>
<th>
<a href="https://github.com/cvxgrp/scs">SCS</a>
<a href="https://github.com/JuliaOpt/SCS.jl">(.jl)</a>
</th>
<!--<td><a href="https://github.com/JuliaOpt/NLopt.jl">NLopt.jl</a></td>-->
<td>✔</td> <!-- LP -->
<td></td> <!-- MILP -->
<td>✔</td> <!-- SOCP -->
<td></td> <!-- MISOCP -->
<td>✔</td> <!-- SDP -->
<td></td> <!-- NLP -->
<td></td> <!-- MINLP -->
<td></td> <!-- Other -->
</tr>
</tbody>
</table>
</div>
</div>
<div class="row">
<div class="col-md-12">
<h3>Papers about JuliaOpt packages</h3>
<ul>
<li>I. Dunning, J. Huchette, and M. Lubin, "JuMP: A modeling language for mathematical optimization". <a href="http://www.optimization-online.org/DB_FILE/2015/04/4891.pdf">[PDF]</a></li>
<li>M. Lubin and I. Dunning, "Computing in Operations Research using Julia". <i>INFORMS Journal on Computing</i> 27(2), pages 238-248, 2015 <a href="http://dx.doi.org/10.1287/ijoc.2014.0623">[DOI]</a> <a href="http://arxiv.org/abs/1312.1431">[arXiv]</a></li>
<li>M. Udell, K. Mohan, D. Zeng, J. Hong, S. Diamond, and S. Boyd, "Convex Optimization in Julia". <i>Proceedings of the 1st First Workshop for High Performance Technical Computing in Dynamic Languages</i>, IEEE Press, 2014. <a href="http://arxiv.org/abs/1410.4821">[arXiv]</a>
</li>
</ul>
<h3>JuliaOpt packages used in courses at</h3>
<ul>
<li>MIT</li>
<li>Sapienza Università di Roma</li>
<li>Stanford University</li>
<li>Universidad Carlos III de Madrid</li>
<li>Université de Liège</li>
<li>University at Buffalo</li>
<li>University of Iowa</li>
<li>University of Southern California</li>
<li>University of South Florida</li>
<li>University of Wisconsin, Madison</li>
<li>Virginia Commonwealth University</li>
</ul>
<h3>Papers using JuliaOpt packages</h3>
<ul>
<li>
R. Brandt and M. Bengtsson, "Fast-Convergent Distributed Coordinated Precoding for TDD Multicell MIMO Systems",
<i>IEEE Int. Workshop Computational Advances in Multi-Sensor Adaptive Process. (CAMSAP'15)</i>, 2015.
<a href="http://kth.diva-portal.org/smash/get/diva2:861877/FULLTEXT01.pdf">[PDF]</a>
<a href="https://github.com/rasmusbrandt/FastConvergentCoordinatedPrecoding.jl">[Code]</a>
</li>
<li>
D. Bertsimas and F. de Ruiter, "Duality in Two-stage Adaptive Linear Optimization: Faster Computation and Stronger Bounds". 2015. <a href="http://www.optimization-online.org/DB_FILE/2015/08/5053.pdf">[PDF]</a>
</li>
<li>
E. Anderes, S. Borgwardt, and J. Miller, "Discrete Wasserstein Barycenters: Optimal Transport for Discrete Data". 2015. <a href="http://arxiv.org/abs/1507.07218">[arXiv]</a>
</li>
<li>
S. D. Gupta, J. K. Tobin, and L. Pavel, "Linear Programming Makes Railway Networks Energy-efficient". 2015. <a href="http://arxiv.org/abs/1506.08243">[arXiv]</a>
</li>
<li>
T. Rossi, R. Pozzi, and M. Testa, "A preliminary proposal to include capacity constraint in the multi-product EOQ model using hybrid systems and integer linear programming". 2015. <a href="http://dx.doi.org/10.1109/IEOM.2015.7093735">[DOI]</a>
</li>
<li>
R. Giordano, T. Broderick, and M. Jordan,
"Linear Response Methods for Accurate Covariance Estimates from Mean Field Variational Bayes". 2015.
<a href="http://arxiv.org/abs/1506.04088">[arXiv]</a>
</li>
<li>
J. Gorham and L. Mackey,
"Measuring Sample Quality with Stein's Method". 2015.
<a href="http://arxiv.org/abs/1506.03039">[arXiv]</a>
</li>
<li>
J. Vielma, I. Dunning, J. Huchette, and M. Lubin,
"Extended Formulations in Mixed Integer Conic Quadratic Programming". 2015.
<a href="http://web.mit.edu/jvielma/www/publications/Extended-Formulations-in-Mixed-Integer-Conic.pdf">[PDF]</a>
</li>
<li>I. Dunning, V. Gupta, A. King, J. Kung, M. Lubin, and J. Silberholz, "A course on advanced software tools for Operations Research and Analytics". <i>INFORMS Transactions on Education</i> 15(2), pages 169-179, 2015. <a href="http://dx.doi.org/10.1287/ited.2014.0131">[DOI]</a> <a href="http://josilber.scripts.mit.edu/IAPEducationPaperDistribute.pdf">[PDF]</a>
</li>
<li>
J. Huchette, M. Lubin, and C. Petra.
"Parallel algebraic modeling for stochastic optimization". 2014.
<i>Proceedings of HPTCDL '14</i>.
<a href="http://www.mcs.anl.gov/~petra/papers/StochJuMP.pdf">[PDF]</a>
</li>
<li>
V. Gupta, "Data-driven models for uncertainty and behavior". 2014. <a href="http://hdl.handle.net/1721.1/91301">[PDF]</a>
</li>
</ul>
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