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<title>HiGHS optimization solver</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">HiGHS optimization solver</span></span>

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</style><table class="infobox vcard"><caption class="infobox-title fn org">HiGHS</caption><tbody><tr><td colspan="2" class="infobox-image logo"><span typeof="mw:File"></span></td></tr><tr><th scope="row" class="infobox-label" style="padding-right:0.6em;">Headquarters</th><td class="infobox-data"><a href="Edinburgh" title="Edinburgh">Edinburgh</a></td></tr><tr><th scope="row" class="infobox-label" style="padding-right:0.6em;">Location</th><td class="infobox-data label"><style data-mw-deduplicate="TemplateStyles:r1126788409">

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</style><div class="plainlist"><ul><li>United Kingdom</li></ul></div></td></tr><tr><th scope="row" class="infobox-label" style="padding-right:0.6em;"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;">Director</div></th><td class="infobox-data">Julian Hall</td></tr><tr><th scope="row" class="infobox-label" style="padding-right:0.6em;"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;">Key people</div></th><td class="infobox-data"><div class="plainlist">

<ul><li>Ivet Galabova</li></ul>

</div></td></tr><tr><th scope="row" class="infobox-label" style="padding-right:0.6em;">Staff</th><td class="infobox-data">6</td></tr><tr><th scope="row" class="infobox-label" style="padding-right:0.6em;">Website</th><td class="infobox-data"><span class="url"><a rel="nofollow" class="external text" href="https://www.highs.dev">www<wbr>.highs<wbr>.dev</a></span></td></tr></tbody></table>

<table class="infobox vevent"><tbody><tr><th colspan="2" class="infobox-above summary">HiGHS</th></tr><tr style="display: none;"><td colspan="2" class="infobox-full-data"></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;"><a href="Software_release_life_cycle" title="Software release life cycle">Stable release</a></th><td class="infobox-data"><div style="margin:0px;">1.10.0

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</td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;"><a href="Repository_(version_control)" title="Repository (version control)">Repository</a></th><td class="infobox-data"><span class="url"><a rel="nofollow" class="external text" href="https://github.com/ERGO-Code/HiGHS">github<wbr>.com<wbr>/ERGO-Code<wbr>/HiGHS</a></span></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;">Written in</th><td class="infobox-data"><a href="C%2B%2B" title="C++">C++</a></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;"><a href="Software_categories#Categorization_approaches" title="Software categories">Type</a></th><td class="infobox-data">Optimization solver suite</td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;"><a href="Software_license" title="Software license">License</a></th><td class="infobox-data"><a href="MIT_License" title="MIT License">MIT</a></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;">Website</th><td class="infobox-data"><span class="url"><a rel="nofollow" class="external text" href="https://ergo-code.github.io/HiGHS">ergo-code<wbr>.github<wbr>.io<wbr>/HiGHS</a></span></td></tr></tbody></table>

<p><b>HiGHS</b> is open-source software to solve <a href="Linear_programming" title="Linear programming">linear programming</a> (LP), <a href="Integer_programming" title="Integer programming">mixed-integer programming</a> (MIP), and convex <a href="Quadratic_programming" title="Quadratic programming">quadratic programming</a> (QP) models.<sup id="cite_ref-hall-2020_1-0" class="reference"><a href="#cite_note-hall-2020-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>

</p><p>Written in <a href="C%2B%2B" title="C++">C++</a> and published under an <a href="MIT_License" title="MIT License">MIT</a> license, HiGHS provides programming interfaces to <a href="C_(programming_language)" title="C (programming language)">C</a>, <a href="Python_(programming_language)" title="Python (programming language)">Python</a>, <a href="Julia_(programming_language)" title="Julia (programming language)">Julia</a>, <a href="Rust_(programming_language)" title="Rust (programming language)">Rust</a>, <a href="R_(programming_language)" title="R (programming language)">R</a>, <a href="JavaScript" title="JavaScript">JavaScript</a>, <a href="Fortran" title="Fortran">Fortran</a>, and <a href="C_Sharp_(programming_language)" title="C Sharp (programming language)">C#</a>. It has no external dependencies. A<span class="nowrap"> </span>convenient thin wrapper to Python is available via the <span class="url"><a rel="nofollow" class="external text" href="https://pypi.org/project/highspy/">highspy</a></span> <a href="Python_Package_Index" title="Python Package Index">PyPI</a> package. HiGHS is also callable via <a href="NuGet" title="NuGet">NuGet</a>.<sup id="cite_ref-nuget-repo_2-0" class="reference"><a href="#cite_note-nuget-repo-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>

</p><p>Although generally single-threaded, some solver components can utilize multi-core architectures and, from <span class="url"><a rel="nofollow" class="external text" href="https://github.com/ERGO-Code/HiGHS/releases/tag/v1.10.0">Version 1.10.0</a></span>, can run its first order LP solver on NVIDIA GPUs. HiGHS is designed to solve large-scale models and exploits <a href="Sparse_matrix" title="Sparse matrix">problem sparsity</a>. Its performance relative to commercial and other open-source software is reviewed periodically using industry-standard <a href="Benchmark_(computing)" title="Benchmark (computing)">benchmarks</a>.<sup id="cite_ref-mittelmann-benchmarks_3-0" class="reference"><a href="#cite_note-mittelmann-benchmarks-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>

</p><p>The term <b>HiGHS</b> may also refer to both the underlying project and the small team leading the software development.

</p>

<div class="mw-heading mw-heading2"><h2 id="History">History</h2></div>

<p>HiGHS is based on solvers written by PhD students from the Optimization and Operational Research Group <sup id="cite_ref-uoe-som-oor_4-0" class="reference"><a href="#cite_note-uoe-som-oor-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> in the School of Mathematics at the <a href="University_of_Edinburgh" title="University of Edinburgh">University of Edinburgh</a>. Its origins can be traced back to late 2016, when Ivet Galabova combined her LP presolve with Julian Hall's simplex crash procedure and Huangfu Qi's dual simplex solver to solve a class of industrial LP problems faster than the best open-source solvers at that time.<sup id="cite_ref-galabova-2022_5-0" class="reference"><a href="#cite_note-galabova-2022-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Since then, a C++<span class="nowrap"> </span><a href="Application_programming_interface" class="mw-redirect" title="Application programming interface">API</a> and other language interfaces have been developed, and modelling utilities and other categories of solver have been added.

</p><p>In early‑2022, the <a href="Open_energy_system_models#GenX" title="Open energy system models">GenX</a> and <a href="Open_energy_system_models#PyPSA" title="Open energy system models">PyPSA</a> open energy system modelling projects endorsed a funding application for the HiGHS solver in an effort to reduce their <a href="Open_Energy_Modelling_Initiative" title="Open Energy Modelling Initiative">community</a> reliance on proprietary libraries.<sup id="cite_ref-parzen-etal-2022_6-0" class="reference"><a href="#cite_note-parzen-etal-2022-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> That appeal resulted in <a href="Canadian_dollar" title="Canadian dollar">CA$</a><span style="margin-right:.25em;">76</span>000 in funding from Invenia Labs, Cambridge, United Kingdom in July<span class="nowrap"> </span>2022.<sup id="cite_ref-invenia-donation_7-0" class="reference"><a href="#cite_note-invenia-donation-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading2"><h2 id="Solvers">Solvers</h2></div>

<div class="mw-heading mw-heading3"><h3 id="Simplex">Simplex</h3></div>

<p>HiGHS has implementations of the primal and dual <a href="Revised_simplex_method" title="Revised simplex method">revised simplex method</a> for solving LP problems, based on techniques described by Hall and McKinnon (2005),<sup id="cite_ref-hall-and-mckinnon-2005_8-0" class="reference"><a href="#cite_note-hall-and-mckinnon-2005-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> and Huangfu and Hall (2015, 2018).<sup id="cite_ref-huangfu-and-hall-2015_9-0" class="reference"><a href="#cite_note-huangfu-and-hall-2015-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-huangfu-and-hall-2018_10-0" class="reference"><a href="#cite_note-huangfu-and-hall-2018-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> These include the exploitation of hyper-sparsity when solving linear systems in the simplex implementations and, for the dual simplex solver, exploitation of multi-threading. The simplex solver's performance relative to commercial and other open-source software is regularly reported using industry-standard benchmarks.<sup id="cite_ref-mittelmann-simplex_11-0" class="reference"><a href="#cite_note-mittelmann-simplex-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading3"><h3 id="Interior_point">Interior point</h3></div>

<p>HiGHS has an <a href="Interior-point_method" title="Interior-point method">interior point method</a> implementation for solving LP problems, based on techniques described by Schork and Gondzio (2020).<sup id="cite_ref-schork-and-gondzio-2020_12-0" class="reference"><a href="#cite_note-schork-and-gondzio-2020-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> It is notable for solving the Newton system iteratively by a <a href="Conjugate_gradient_method#The_preconditioned_conjugate_gradient_method" title="Conjugate gradient method">preconditioned conjugate gradient</a> method, rather than directly, via an <a href="Cholesky_decomposition#LDL_decomposition" title="Cholesky decomposition">LDL*</a> decomposition. The interior point solver's performance relative to commercial and other open-source software is regularly reported using industry-standard benchmarks.<sup id="cite_ref-mittelmann-barrier_13-0" class="reference"><a href="#cite_note-mittelmann-barrier-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading3"><h3 id="Mixed_integer_programming">Mixed integer programming</h3></div>

<p>HiGHS has a <a href="Branch_and_cut" title="Branch and cut">branch-and-cut</a> solver for MIP problems. Its performance relative to commercial and other open-source software is regularly reported using industry-standard benchmarks.<sup id="cite_ref-mittelmann-mip_14-0" class="reference"><a href="#cite_note-mittelmann-mip-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading3"><h3 id="Quadratic_programming">Quadratic programming</h3></div>

<p>HiGHS has an active set solver for convex <a href="Quadratic_programming" title="Quadratic programming">quadratic programming</a> (QP) problems.

</p>

<div class="mw-heading mw-heading2"><h2 id="Applications_using_HiGHS">Applications using HiGHS</h2></div>

<p>HiGHS can be used as a stand‑alone solver library in bespoke applications, but numerical computing environments, optimization programming packages, and domain‑specific numerical analysis projects are starting to incorporate the software into their systems also.

</p>

<div class="mw-heading mw-heading3"><h3 id="Numerical_computing_support">Numerical computing support</h3></div>

<p>As powerful open‑source software under active development, HiGHS is increasingly being adopted by <a href="Application_software" title="Application software">application software</a> projects that provide support for <a href="Numerical_analysis" title="Numerical analysis">numerical analysis</a>. The <a href="SciPy" title="SciPy">SciPy</a> scientific library, for instance, uses HiGHS as its LP solver <sup id="cite_ref-scipy-linprog_15-0" class="reference"><a href="#cite_note-scipy-linprog-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> from release<span class="nowrap"> </span>1.6.0 <sup id="cite_ref-scipy-1.6.0-lp_16-0" class="reference"><a href="#cite_note-scipy-1.6.0-lp-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> and the HiGHS MIP solver for <a href="Discrete_optimization" title="Discrete optimization">discrete optimization</a> from release<span class="nowrap"> </span>1.9.0.<sup id="cite_ref-scipy-1.9.0-mip_17-0" class="reference"><a href="#cite_note-scipy-1.9.0-mip-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> As well as offering an interface to HiGHS, the <a href="JuMP" title="JuMP">JuMP</a> modelling language for <a href="Julia_(programming_language)" title="Julia (programming language)">Julia</a> <sup id="cite_ref-jump-home_18-0" class="reference"><a href="#cite_note-jump-home-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> also describes the specific use of HiGHS in its user documentation.<sup id="cite_ref-jump-models_19-0" class="reference"><a href="#cite_note-jump-models-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> The MIP solver in the <a href="NAG_Numerical_Library" title="NAG Numerical Library">NAG</a> library is based on HiGHS ,<sup id="cite_ref-nag-h02bkf_20-0" class="reference"><a href="#cite_note-nag-h02bkf-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> and HiGHS is the default LP and MIP solver in the <span class="nowrap"> </span><a href="MathWorks" title="MathWorks">MathWorks</a> Optimization Toolbox .<sup id="cite_ref-mathworks-R2024a_21-0" class="reference"><a href="#cite_note-mathworks-R2024a-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading3"><h3 id="Open_energy_system_models">Open energy system models</h3></div>

<p>HiGHS is now also used by some domain‑specific applications, including one <a href="Open_energy_system_models" title="Open energy system models">open energy system modeling</a> environment. The web‑based version of the <a href="Open_energy_system_models#PyPSA" title="Open energy system models">PyPSA</a> European multi‑sector model deploys the HiGHS solver by default from February 2022.<sup id="cite_ref-brown-ongoing_22-0" class="reference"><a href="#cite_note-brown-ongoing-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-pypsa-server-diff-feb-2022_23-0" class="reference"><a href="#cite_note-pypsa-server-diff-feb-2022-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> The GridCal project developing research‑oriented power systems software added optional support for HiGHS in February<span class="nowrap"> </span>2022.<sup id="cite_ref-gridcal-diff-feb-2022_24-0" class="reference"><a href="#cite_note-gridcal-diff-feb-2022-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup>

</p>

<ul><li><a href="List_of_optimization_software" title="List of optimization software">List of optimization software</a></li>

<li><a href="Mathematical_optimization" title="Mathematical optimization">Mathematical optimization</a></li>

<li><a href="Benchmark_(computing)" title="Benchmark (computing)">Numerical benchmarking</a></li>

<li><a href="Simplex_algorithm" title="Simplex algorithm">Simplex method</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li><a rel="nofollow" class="external text" href="https://github.com/ERGO-Code/HiGHS">GitHub repository</a></li>

<li><a rel="nofollow" class="external text" href="https://ergo-code.github.io/HiGHS">Software documentation</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite id="CITEREFHall2020" class="citation book cs1">Hall, Julian (21 September 2020). <a rel="nofollow" class="external text" href="https://co-at-work.zib.de/slides/Montag_21.9/HiGHS%20slides%20%281%29.pdf"><i>HiGHS: High-performance open-source software for linear optimization</i></a> <span class="cs1-format">(PDF)</span>. Edinburgh, United Kingdom: University of Edinburgh<span class="reference-accessdate">. Retrieved <span class="nowrap">27 February</span> 2022</span>.</cite> Presentation.</span>

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<cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://nuget.org/packages/Highs.Native/">"Highs.Native"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">13 May</span> 2025</span>.</cite></span>

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<cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://plato.asu.edu/bench.html">"Benchmarks for optimization software"</a>. <i>Decision tree for optimization software</i>. March 2022<span class="reference-accessdate">. Retrieved <span class="nowrap">31 March</span> 2022</span>.</cite></span>

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<cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.maths.ed.ac.uk/school-of-mathematics/research/data-decisions/optimization-and-operational-research">"Optimization and Operational Research: School of Mathematics"</a>. March 2022<span class="reference-accessdate">. Retrieved <span class="nowrap">31 March</span> 2022</span>.</cite></span>

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<cite id="CITEREFGalabova2022" class="citation thesis cs1">Galabova, Ivet (2022). <a rel="nofollow" class="external text" href="https://era.ed.ac.uk/bitstream/handle/1842/39725/GalabovaI_2022.pdf"><i>Presolve, crash and software engineering for HiGHS</i></a> <span class="cs1-format">(PDF)</span> (PhD). Edinburgh, United Kingdom: The University of Edinburgh<span class="reference-accessdate">. Retrieved <span class="nowrap">13 May</span> 2025</span>.</cite></span>

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<cite id="CITEREFParzenHallJenkinsBrown2022" class="citation book cs1">Parzen, Maximilian; Hall, Julian; Jenkins, Jesse; Brown, Tom (31 March 2022). <a rel="nofollow" class="external text" href="https://zenodo.org/record/6409433"><i>Optimization solvers: the missing link for a fully open-source energy system modelling ecosystem</i></a> <span class="cs1-format">(PDF)</span>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.5281%2Fzenodo.6409432">10.5281/zenodo.6409432</a><span class="reference-accessdate">. Retrieved <span class="nowrap">3 April</span> 2022</span>.</cite> Eight page funding proposal which also offers a relatively detailed roadmap. <span style="position:relative; top: -2px;"><span typeof="mw:File"><a href="Open_access" title="open access publication – free to read"></a></span></span></span>

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<cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.maths.ed.ac.uk/school-of-mathematics/news?nid=974">"A $76k donation from Invenia Labs has been received to support HiGHS"</a>. <i>School of Mathematics, Edinburgh University</i>. Edinburgh, Scotland. 21 July 2022<span class="reference-accessdate">. Retrieved <span class="nowrap">21 July</span> 2022</span>.</cite></span>

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<cite id="CITEREFHallMcKinnon2005" class="citation journal cs1">Hall, JAJ; McKinnon, KIM (1 December 2005). <a rel="nofollow" class="external text" href="https://www.optimization-online.org/DB_FILE/2000/11/234.pdf">"Hyper-sparsity in the revised Simplex method and how to exploit it"</a> <span class="cs1-format">(PDF)</span>. <i>Computational Optimization and Applications</i>. <b>32</b> (3): <span class="nowrap">259–</span>283. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs10589-005-4802-0">10.1007/s10589-005-4802-0</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1573-2894">1573-2894</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:15967632">15967632</a><span class="reference-accessdate">. Retrieved <span class="nowrap">1 April</span> 2022</span>.</cite> Linked PDF is an early preprint.</span>

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<cite id="CITEREFHuangfuHall2015" class="citation journal cs1">Huangfu, Q; Hall, JAJ (April 2015). <a rel="nofollow" class="external text" href="https://link.springer.com/content/pdf/10.1007/s10589-014-9689-1.pdf">"Novel update techniques for the revised simplex method"</a> <span class="cs1-format">(PDF)</span>. <i>Computational Optimization and Applications</i>. <b>60</b> (3): <span class="nowrap">587–</span>608. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs10589-014-9689-1">10.1007/s10589-014-9689-1</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0926-6003">0926-6003</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:254416722">254416722</a><span class="reference-accessdate">. Retrieved <span class="nowrap">31 March</span> 2022</span>.</cite></span>

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<li id="cite_note-mittelmann-simplex-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-mittelmann-simplex_11-0">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20211111222213/http://plato.asu.edu/ftp/lpsimp.html">"Benchmark of Simplex LP solvers"</a>. <i>Decision tree for optimization software</i>. March 2022. Archived from <a rel="nofollow" class="external text" href="http://plato.asu.edu/ftp/lpsimp.html">the original</a> on 11 November 2021<span class="reference-accessdate">. Retrieved <span class="nowrap">31 March</span> 2022</span>.</cite></span>

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<cite id="CITEREFSchorkGondzio2020" class="citation journal cs1">Schork, Lukas; Gondzio, Jacek (December 2020). <a rel="nofollow" class="external text" href="https://link.springer.com/content/pdf/10.1007/s12532-020-00181-8.pdf">"Implementation of an interior point method with basis preconditioning"</a> <span class="cs1-format">(PDF)</span>. <i>Mathematical Programming Computation</i>. <b>12</b> (4): <span class="nowrap">603–</span>635. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs12532-020-00181-8">10.1007/s12532-020-00181-8</a>. <a href="Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<a rel="nofollow" class="external text" href="https://hdl.handle.net/20.500.11820%2F00a692a1-3372-41f6-8baf-f45396efcc0e">20.500.11820/00a692a1-3372-41f6-8baf-f45396efcc0e</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1867-2949">1867-2949</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:53444331">53444331</a><span class="reference-accessdate">. Retrieved <span class="nowrap">31 March</span> 2022</span>.</cite></span>

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<cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://plato.asu.edu/ftp/lpbar.html">"Benchmark of Barrier LP solvers"</a>. <i>Decision tree for optimization software</i>. March 2022<span class="reference-accessdate">. Retrieved <span class="nowrap">31 March</span> 2022</span>.</cite></span>

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<cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://jump.dev">"JuMP"</a>. <i>JuMP</i>. March 2022<span class="reference-accessdate">. Retrieved <span class="nowrap">1 April</span> 2022</span>.</cite></span>

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</ol></div>

<p><br>

</p>

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</style><div id="Mathematical_optimization_software220" style="font-size:114%;margin:0 4em"><a href="List_of_optimization_software" title="List of optimization software">Mathematical optimization software</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;">Data formats</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Mathematica" class="mw-redirect" title="Mathematica">Mathematica</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;"><a href="Mathematical_modeling" class="mw-redirect" title="Mathematical modeling">Modeling</a> tools</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="AIMMS" title="AIMMS">AIMMS</a></li>

<li><a href="APMonitor" title="APMonitor">APMonitor</a></li>

<li><a href="ECLiPSe" title="ECLiPSe">ECLiPSe</a>-CLP</li>

<li><a href="Gekko_(optimization_software)" title="Gekko (optimization software)">Gekko</a></li>

<li><a href="GNU_Linear_Programming_Kit" title="GNU Linear Programming Kit">GNU MathProg</a></li>

<li><a href="LINDO" title="LINDO">LINDO</a></li>

<li><a href="Mathematica" class="mw-redirect" title="Mathematica">Mathematica</a></li>

<li><a href="MiniZinc" title="MiniZinc">MiniZinc</a></li>

<li><a href="OptimJ" title="OptimJ">OptimJ</a></li>

<li><a href="Pyomo" title="Pyomo">Pyomo</a></li>

<li><a href="TOMLAB" title="TOMLAB">TOMLAB</a></li>

<li><a href="FICO_Xpress" title="FICO Xpress">Xpress Mosel</a></li>

<li><a href="SCIP_(optimization_software)" class="mw-redirect" title="SCIP (optimization software)">ZIMPL</a></li>

<li><a href="CasADi" title="CasADi">CasADi</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;"><a href="Solver" title="Solver">Solvers</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Linear_programming" title="Linear programming">LP</a>, <a href="Linear_programming#Integer_unknowns" title="Linear programming">MILP</a><sup style="font-weight:normal;">∗</sup></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="APOPT" title="APOPT">APOPT</a><sup>∗</sup></li>

<li><a href="ANTIGONE" title="ANTIGONE">ANTIGONE</a><sup>∗</sup></li>

<li><a href="Artelys_Knitro" title="Artelys Knitro">Artelys Knitro</a><sup>∗</sup></li>

<li><a href="CPLEX" title="CPLEX">CPLEX</a><sup>∗</sup></li>

<li><a href="FortMP" title="FortMP">FortMP</a><sup>∗</sup></li>

<li><a href="GNU_Linear_Programming_Kit" title="GNU Linear Programming Kit">GLPK/GLPSOL</a><sup>∗</sup></li>

<li><a href="Gurobi_Optimizer" title="Gurobi Optimizer">Gurobi Optimizer</a><sup>∗</sup></li>

<li><a href="LINDO" title="LINDO">LINDO</a><sup>∗</sup></li>

<li><a href="Lp_solve" title="Lp solve">Lp_solve</a></li>

<li><a href="Mathematica" class="mw-redirect" title="Mathematica">Mathematica</a></li>

<li><a href="MINOS_(optimization_software)" title="MINOS (optimization software)">MINOS</a></li>

<li><a href="MINTO" title="MINTO">MINTO</a><sup>∗</sup></li>

<li><a href="MOSEK" title="MOSEK">MOSEK</a><sup>∗</sup></li>

<li><a href="SCIP_(optimization_software)" class="mw-redirect" title="SCIP (optimization software)">SoPlex</a></li>

<li><a href="Octeract_Engine" title="Octeract Engine">Octeract Engine</a><sup>∗</sup></li>

<li><a href="COIN-OR#SYMPHONY" title="COIN-OR">SYMPHONY</a><sup>∗</sup></li>

<li><a href="FICO_Xpress" title="FICO Xpress">Xpress Optimizer</a><sup>∗</sup></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Quadratic_programming" title="Quadratic programming">QP</a>, MIQP<sup style="font-weight:normal;">∗</sup></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="APOPT" title="APOPT">APOPT</a><sup>∗</sup></li>

<li><a href="ANTIGONE" title="ANTIGONE">ANTIGONE</a><sup>∗</sup></li>

<li><a href="Artelys_Knitro" title="Artelys Knitro">Artelys Knitro</a><sup>∗</sup></li>

<li><a href="CPLEX" title="CPLEX">CPLEX</a><sup>∗</sup></li>

<li><a href="FortMP" title="FortMP">FortMP</a><sup>∗</sup></li>

<li><a href="Gurobi_Optimizer" title="Gurobi Optimizer">Gurobi Optimizer</a><sup>∗</sup></li>

<li><a href="IPOPT" title="IPOPT">IPOPT</a></li>

<li><a href="LINDO" title="LINDO">LINDO</a><sup>∗</sup></li>

<li><a href="Mathematica" class="mw-redirect" title="Mathematica">Mathematica</a></li>

<li><a href="MINOS_(optimization_software)" title="MINOS (optimization software)">MINOS</a></li>

<li><a href="MOSEK" title="MOSEK">MOSEK</a><sup>∗</sup></li>

<li><a href="Octeract_Engine" title="Octeract Engine">Octeract Engine</a><sup>∗</sup></li>

<li><a href="FICO_Xpress" title="FICO Xpress">Xpress Optimizer</a><sup>∗</sup></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Quadratically_constrained_quadratic_program" title="Quadratically constrained quadratic program">QCP</a>, MIQCP<sup style="font-weight:normal;">∗</sup></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="APOPT" title="APOPT">APOPT</a><sup>∗</sup></li>

<li><a href="ANTIGONE" title="ANTIGONE">ANTIGONE</a><sup>∗</sup></li>

<li><a href="Artelys_Knitro" title="Artelys Knitro">Artelys Knitro</a><sup>∗</sup></li>

<li><a href="CPLEX" title="CPLEX">CPLEX</a><sup>∗</sup></li>

<li><a href="Gurobi_Optimizer" title="Gurobi Optimizer">Gurobi Optimizer</a><sup>∗</sup></li>

<li><a href="IPOPT" title="IPOPT">IPOPT</a></li>

<li><a href="LINDO" title="LINDO">LINDO</a><sup>∗</sup></li>

<li><a href="Mathematica" class="mw-redirect" title="Mathematica">Mathematica</a></li>

<li><a href="MINOS_(optimization_software)" title="MINOS (optimization software)">MINOS</a></li>

<li><a href="MOSEK" title="MOSEK">MOSEK</a><sup>∗</sup></li>

<li><a href="Octeract_Engine" title="Octeract Engine">Octeract Engine</a><sup>∗</sup></li>

<li><a href="FICO_Xpress" title="FICO Xpress">Xpress Optimizer</a><sup>∗</sup></li>

<li><a href="FICO_Xpress" title="FICO Xpress">Xpress NonLinear</a><sup>∗</sup></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Second-order_cone_programming" title="Second-order cone programming">SOCP</a>, MISOCP<sup style="font-weight:normal;">∗</sup></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Artelys_Knitro" title="Artelys Knitro">Artelys Knitro</a><sup>∗</sup></li>

<li><a href="CPLEX" title="CPLEX">CPLEX</a><sup>∗</sup></li>

<li><a href="Gurobi_Optimizer" title="Gurobi Optimizer">Gurobi Optimizer</a><sup>∗</sup></li>

<li><a href="LINDO" title="LINDO">LINDO</a><sup>∗</sup></li>

<li><a href="Mathematica" class="mw-redirect" title="Mathematica">Mathematica</a></li>

<li><a href="MOSEK" title="MOSEK">MOSEK</a><sup>∗</sup></li>

<li><a href="FICO_Xpress" title="FICO Xpress">Xpress Optimizer</a><sup>∗</sup></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Semidefinite_programming" title="Semidefinite programming">SDP</a>, MISDP<sup style="font-weight:normal;">∗</sup></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Mathematica" class="mw-redirect" title="Mathematica">Mathematica</a></li>

<li><a href="MOSEK" title="MOSEK">MOSEK</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Nonlinear_programming" title="Nonlinear programming">NLP</a>, MINLP<sup style="font-weight:normal;">∗</sup></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="APOPT" title="APOPT">APOPT</a><sup>∗</sup></li>

<li><a href="ANTIGONE" title="ANTIGONE">ANTIGONE</a><sup>∗</sup></li>

<li><a href="Artelys_Knitro" title="Artelys Knitro">Artelys Knitro</a><sup>∗</sup></li>

<li><a href="BARON" title="BARON">BARON</a><sup>∗</sup></li>

<li><a href="Couenne" title="Couenne">Couenne</a><sup>∗</sup></li>

<li><a href="Galahad_library" title="Galahad library">Galahad library</a></li>

<li><a href="Gurobi_Optimizer" title="Gurobi Optimizer">Gurobi Optimizer</a><sup>∗</sup></li>

<li><a href="IPOPT" title="IPOPT">IPOPT</a></li>

<li><a href="LINDO" title="LINDO">LINDO</a><sup>∗</sup></li>

<li><a href="MIDACO" title="MIDACO">MIDACO</a><sup>∗</sup></li>

<li><a href="MINOS_(optimization_software)" title="MINOS (optimization software)">MINOS</a></li>

<li><a href="NLPQLP" title="NLPQLP">NLPQLP</a></li>

<li><a href="NPSOL" title="NPSOL">NPSOL</a></li>

<li><a href="SNOPT" title="SNOPT">SNOPT</a><sup>∗</sup></li>

<li><a href="Octeract_Engine" title="Octeract Engine">Octeract Engine</a><sup>∗</sup></li>

<li><a href="WORHP" title="WORHP">WORHP</a></li>

<li><a href="FICO_Xpress" title="FICO Xpress">Xpress NonLinear</a><sup>∗</sup></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Global_optimization" title="Global optimization">GO</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="ANTIGONE" title="ANTIGONE">ANTIGONE</a><sup>∗</sup></li>

<li><a href="BARON" title="BARON">BARON</a></li>

<li><a href="Couenne" title="Couenne">Couenne</a><sup>∗</sup></li>

<li><a href="FICO_Xpress" title="FICO Xpress">Xpress Global</a></li>

<li><a href="Mathematica" class="mw-redirect" title="Mathematica">Mathematica</a></li>

<li><a href="LINDO" title="LINDO">LINDO</a></li>

<li><a href="Octeract_Engine" title="Octeract Engine">Octeract Engine</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Constraint_programming" title="Constraint programming">CP</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li>Artelys Kalis</li>

<li>Comet</li>

<li><a href="CPLEX" title="CPLEX">CPLEX</a> CP Optimizer</li>

<li><a href="Gecode" title="Gecode">Gecode</a></li>

<li><a href="Mathematica" class="mw-redirect" title="Mathematica">Mathematica</a></li>

<li><a href="JaCoP_(solver)" title="JaCoP (solver)">JaCoP</a></li>

<li><a href="FICO_Xpress" title="FICO Xpress">Xpress Kalis</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div>

<ul><li><b><a href="List_of_optimization_software" title="List of optimization software">List of optimization software</a></b></li>

<li><b><a href="Comparison_of_optimization_software" title="Comparison of optimization software">Comparison of optimization software</a></b></li></ul>

</div></td></tr></tbody></table></div>

<div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="Scientific_modelling114" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Scientific_modelling114" style="font-size:114%;margin:0 4em"><a href="Scientific_modelling" title="Scientific modelling">Scientific modelling</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Modelling_biological_systems" title="Modelling biological systems">Biological</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Cellular_model" title="Cellular model">Cellular model</a></li>

<li><a href="Chemical_process_modeling" title="Chemical process modeling">Chemical process modeling</a></li>

<li><a href="Ecosystem_model" title="Ecosystem model">Ecosystem model</a></li>

<li><a href="Mathematical_modelling_of_infectious_disease" class="mw-redirect" title="Mathematical modelling of infectious disease">Infectious disease model</a></li>

<li><a href="Metabolic_network_modelling" title="Metabolic network modelling">Metabolic network modelling</a></li>

<li><a href="Modelling_biological_systems" title="Modelling biological systems">Modelling biological systems</a></li>

<li><a href="Protein_structure_prediction" title="Protein structure prediction">Protein structure prediction</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Environmental</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Atmospheric_model" title="Atmospheric model">Atmospheric model</a></li>

<li><a href="Chemical_transport_model" title="Chemical transport model">Chemical transport model</a></li>

<li><a href="Climate_model" title="Climate model">Climate model</a></li>

<li><a href="Geologic_modelling" class="mw-redirect" title="Geologic modelling">Geologic modelling</a></li>

<li><a href="Groundwater_model" title="Groundwater model">Groundwater model</a></li>

<li><a href="Hydrological_model" title="Hydrological model">Hydrological model</a></li>

<li><a href="Hydrological_transport_model" title="Hydrological transport model">Hydrological transport model</a></li>

<li><a href="Modular_Ocean_Model" title="Modular Ocean Model">Modular Ocean Model</a></li>

<li><a href="Wildfire_modeling" title="Wildfire modeling">Wildfire modeling</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Sustainability</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Energy_modeling" title="Energy modeling">Energy modeling</a></li>

<li><a href="Integrated_assessment_modelling" title="Integrated assessment modelling">Integrated assessment modelling</a></li>

<li><a href="Population_model" title="Population model">Population model</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Social</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Biopsychosocial_model" title="Biopsychosocial model">Biopsychosocial model</a></li>

<li><a href="Business_process_modelling" class="mw-redirect" title="Business process modelling">Business process modelling</a></li>

<li><a href="Catastrophe_modeling" title="Catastrophe modeling">Catastrophe modeling</a></li>

<li><a href="Construction_and_management_simulation" title="Construction and management simulation">Construction and management simulation</a></li>

<li><a href="Crime_mapping" title="Crime mapping">Crime mapping</a></li>

<li><a href="Economic_model" title="Economic model">Economic model</a></li>

<li><a href="Input%E2%80%93output_model" title="Input–output model">Input–output model</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related topics</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Data_visualization" class="mw-redirect" title="Data visualization">Data visualization</a></li>

<li><a href="List_of_computer_simulation_software" title="List of computer simulation software">List of computer simulation software</a></li>

<li><a href="Mathematical_modeling" class="mw-redirect" title="Mathematical modeling">Mathematical modeling</a></li>

<li><a href="Systems_theory" title="Systems theory">Systems theory</a></li>

<li><a href="Systems_thinking" title="Systems thinking">Systems thinking</a></li>

<li><a href="Visual_analytics" title="Visual analytics">Visual analytics</a></li></ul>

</div></td></tr></tbody></table></div>

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