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class="firstHeading mw-first-heading"><span class="mw-page-title-main">APOPT</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="This article exist only in this language. 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<div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox vevent"><caption class="infobox-title summary">APOPT</caption><tbody><tr><th scope="row" class="infobox-label" style="white-space: nowrap;"><a href="/wiki/Programmer" title="Programmer">Developer(s)</a></th><td class="infobox-data"><span class="url"><a rel="nofollow" class="external text" href="http://apopt.com">Advanced Process Solutions, LLC</a></span></td></tr><tr style="display: none;"><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546" /></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;"><a href="/wiki/Software_release_life_cycle" title="Software release life cycle">Stable release</a></th><td class="infobox-data"><div style="margin:0px;">1.0.4 / October 1, 2021<span class="noprint">; 3 years ago</span><span style="display:none"> (<span class="bday dtstart published updated">2021-10-01</span>)</span></div></td></tr><tr style="display:none"><td colspan="2"> </td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;"><a href="/wiki/Operating_system" title="Operating system">Operating system</a></th><td class="infobox-data"><span class="url"><a rel="nofollow" class="external text" href="http://apopt.com/developers.php">Cross-Platform</a></span></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;"><a href="/wiki/Software_categories#Categorization_approaches" title="Software categories">Type</a></th><td class="infobox-data"><a href="/wiki/List_of_numerical_analysis_software" class="mw-redirect" title="List of numerical analysis software">Technical computing</a></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;"><a href="/wiki/Software_license" title="Software license">License</a></th><td class="infobox-data"><a href="/wiki/Proprietary_software" title="Proprietary software">Proprietary</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="http://apopt.com">apopt<wbr />.com</a></span></td></tr></tbody></table> <p><b>APOPT</b> (for <b>Advanced Process OPTimizer</b>) is a software package for solving large-scale <a href="/wiki/Optimization_(mathematics)" class="mw-redirect" title="Optimization (mathematics)">optimization</a> problems of any of these forms: </p> <ul><li><a href="/wiki/Linear_programming" title="Linear programming">Linear programming</a> (LP)</li> <li><a href="/wiki/Quadratic_programming" title="Quadratic programming">Quadratic programming</a> (QP)</li> <li><a href="/wiki/Quadratically_constrained_quadratic_program" title="Quadratically constrained quadratic program">Quadratically constrained quadratic program</a> (QCQP)</li> <li><a href="/wiki/Nonlinear_programming" title="Nonlinear programming">Nonlinear programming</a> (NLP)</li> <li><a href="/wiki/Mixed_integer_programming" class="mw-redirect" title="Mixed integer programming">Mixed integer programming</a> (MIP)</li> <li><a href="/wiki/Mixed_integer_linear_programming" class="mw-redirect" title="Mixed integer linear programming">Mixed integer linear programming</a> (MILP)</li> <li><a href="/w/index.php?title=Mixed_integer_nonlinear_programming&action=edit&redlink=1" class="new" title="Mixed integer nonlinear programming (page does not exist)">Mixed integer nonlinear programming</a> (MINLP)</li></ul> <p>Applications of the APOPT include <a href="/wiki/Chemical_reactor" title="Chemical reactor">chemical reactors</a>,<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Friction_stir_welding" title="Friction stir welding">friction stir welding</a>,<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> prevention of hydrate formation in deep-sea pipelines,<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Computational_biology" title="Computational biology">computational biology</a>,<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Solid_oxide_fuel_cell" title="Solid oxide fuel cell">solid oxide fuel cells</a>,<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> and flight controls for <a href="/wiki/Unmanned_aerial_vehicle" title="Unmanned aerial vehicle">Unmanned Aerial Vehicles (UAVs)</a>.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Benchmark_Testing">Benchmark Testing</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=APOPT&action=edit&section=1" title="Edit section: Benchmark Testing"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Standard benchmarks such as <a href="/wiki/CUTEr" title="CUTEr">CUTEr</a> and <a href="/wiki/SBML" title="SBML">SBML</a> curated models are used to test the performance of APOPT relative to solvers <a href="/w/index.php?title=BPOPT&action=edit&redlink=1" class="new" title="BPOPT (page does not exist)">BPOPT</a>, <a href="/wiki/IPOPT" title="IPOPT">IPOPT</a>, <a href="/wiki/SNOPT" title="SNOPT">SNOPT</a>, and <a href="/wiki/MINOS_(optimization_software)" title="MINOS (optimization software)">MINOS</a>. A combination of APOPT (Active Set SQP) and <a href="/w/index.php?title=BPOPT&action=edit&redlink=1" class="new" title="BPOPT (page does not exist)">BPOPT</a> (Interior Point Method) performed the best on 494 benchmark problems for solution speed and total fraction of problems solved.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=APOPT&action=edit&section=2" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>APOPT is supported in <a href="/wiki/AMPL" title="AMPL">AMPL</a>, <a href="/wiki/APMonitor" title="APMonitor">APMonitor</a>, <a href="/wiki/Gekko_(optimization_software)" title="Gekko (optimization software)">Gekko</a>, <a href="/wiki/Julia_(programming_language)" title="Julia (programming language)">Julia</a>, <a href="/wiki/MATLAB" title="MATLAB">MATLAB</a>, <a href="/wiki/Pyomo" title="Pyomo">Pyomo</a>, and <a href="/wiki/Python_(programming_language)" title="Python (programming language)">Python</a>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=APOPT&action=edit&section=3" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1041539562">.mw-parser-output .citation{word-wrap:break-word}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}</style><span class="citation patent" id="CITEREFLawson,_K._W.,_Hedengren,_J._D.,_Smith,_L._C.2012"><a rel="nofollow" class="external text" href="https://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=WO2012005740">WO patent 2012005740</a>, Lawson, K. W., Hedengren, J. D., Smith, L. C., "Method for Controlling Bubble Formation in Polymerization Reactors", published 2012-01-12</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Apatent&rft.number=2012005740&rft.cc=WO&rft.title=Method+for+Controlling+Bubble+Formation+in+Polymerization+Reactors&rft.inventor=Lawson%2C+K.+W.%2C+Hedengren%2C+J.+D.%2C+Smith%2C+L.+C.&rft.pubdate=2012-01-12"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFSpivey2010" class="citation journal cs1">Spivey, B. 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(2013). <a rel="nofollow" class="external text" href="http://apm.byu.edu/prism/uploads/Members/sun_2013.pdf">"Optimal Trajectory Generation using Model Predictive Control for Aerially Towed Cable Systems"</a> <span class="cs1-format">(PDF)</span>. <i>Journal of Guidance, Control, and Dynamics</i>. <b>37</b> (2): 525. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2014JGCD...37..525S">2014JGCD...37..525S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2514%2F1.60820">10.2514/1.60820</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Guidance%2C+Control%2C+and+Dynamics&rft.atitle=Optimal+Trajectory+Generation+using+Model+Predictive+Control+for+Aerially+Towed+Cable+Systems&rft.volume=37&rft.issue=2&rft.pages=525&rft.date=2013&rft_id=info%3Adoi%2F10.2514%2F1.60820&rft_id=info%3Abibcode%2F2014JGCD...37..525S&rft.aulast=Sun&rft.aufirst=L.&rft_id=http%3A%2F%2Fapm.byu.edu%2Fprism%2Fuploads%2FMembers%2Fsun_2013.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAPOPT" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFHedengren2012" class="citation journal cs1">Hedengren, J. 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style="padding:0 0.25em"> <ul><li><a href="/wiki/Mathematica" class="mw-redirect" title="Mathematica">Mathematica</a></li> <li><a href="/wiki/MPS_(format)" title="MPS (format)">MPS</a></li> <li><a href="/wiki/Nl_(format)" title="Nl (format)">nl</a></li> <li><a href="/wiki/Sol_(format)" title="Sol (format)">sol</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;"><a href="/wiki/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="/wiki/AIMMS" title="AIMMS">AIMMS</a></li> <li><a href="/wiki/AMPL" title="AMPL">AMPL</a></li> <li><a href="/wiki/APMonitor" title="APMonitor">APMonitor</a></li> <li><a href="/wiki/ECLiPSe" title="ECLiPSe">ECLiPSe</a>-CLP</li> <li><a href="/wiki/Gekko_(optimization_software)" title="Gekko (optimization software)">Gekko</a></li> <li><a href="/wiki/General_Algebraic_Modeling_System" class="mw-redirect" title="General Algebraic Modeling System">GAMS</a></li> <li><a href="/wiki/GNU_Linear_Programming_Kit" title="GNU Linear Programming Kit">GNU MathProg</a></li> <li><a href="/wiki/JuMP" title="JuMP">JuMP</a></li> <li><a href="/wiki/LINDO" title="LINDO">LINDO</a></li> <li><a href="/wiki/CPLEX" title="CPLEX">OPL</a></li> <li><a href="/wiki/Mathematica" class="mw-redirect" title="Mathematica">Mathematica</a></li> <li><a href="/wiki/MiniZinc" title="MiniZinc">MiniZinc</a></li> <li><a href="/wiki/OptimJ" title="OptimJ">OptimJ</a></li> <li><a href="/wiki/COIN-OR#PuLP" title="COIN-OR">PuLP</a></li> <li><a href="/wiki/Pyomo" title="Pyomo">Pyomo</a></li> <li><a href="/wiki/TOMLAB" title="TOMLAB">TOMLAB</a></li> <li><a href="/wiki/FICO_Xpress" title="FICO Xpress">Xpress Mosel</a></li> <li><a href="/wiki/SCIP_(optimization_software)#SCIP_Optimization_Suite" class="mw-redirect" title="SCIP (optimization software)">ZIMPL</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;"><a href="/wiki/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="/wiki/Linear_programming" title="Linear programming">LP</a>, <a href="/wiki/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 class="mw-selflink selflink">APOPT</a><sup>∗</sup></li> <li><a href="/wiki/ANTIGONE" title="ANTIGONE">ANTIGONE</a><sup>∗</sup></li> <li><a href="/wiki/Artelys_Knitro" title="Artelys Knitro">Artelys Knitro</a><sup>∗</sup></li> <li><a href="/wiki/COIN-OR" title="COIN-OR">BCP</a><sup>∗</sup></li> <li><a href="/wiki/COIN-OR#CLP" title="COIN-OR">CLP</a></li> <li><a href="/wiki/COIN-OR#CBC" title="COIN-OR">CBC</a><sup>∗</sup></li> <li><a href="/wiki/CPLEX" title="CPLEX">CPLEX</a><sup>∗</sup></li> <li><a href="/wiki/FortMP" title="FortMP">FortMP</a><sup>∗</sup></li> <li><a href="/wiki/SCIP_(optimization_software)#SCIP_Optimization_Suite" class="mw-redirect" title="SCIP (optimization software)">GCG</a><sup>∗</sup></li> <li><a href="/wiki/GLOP" title="GLOP">GLOP</a><sup>∗</sup></li> <li><a href="/wiki/GNU_Linear_Programming_Kit" title="GNU Linear Programming Kit">GLPK/GLPSOL</a><sup>∗</sup></li> <li><a href="/wiki/Gurobi_Optimizer" title="Gurobi Optimizer">Gurobi Optimizer</a><sup>∗</sup></li> <li><a href="/wiki/HiGHS_optimization_solver" title="HiGHS optimization solver">HiGHS</a><sup>∗</sup></li> <li><a href="/wiki/LINDO" title="LINDO">LINDO</a><sup>∗</sup></li> <li><a href="/wiki/Lp_solve" title="Lp solve">Lp_solve</a></li> <li><a href="/wiki/Robert_J._Vanderbei" title="Robert J. Vanderbei">LOQO</a></li> <li><a href="/wiki/Mathematica" class="mw-redirect" title="Mathematica">Mathematica</a></li> <li><a href="/wiki/MINOS_(optimization_software)" title="MINOS (optimization software)">MINOS</a></li> <li><a href="/wiki/MINTO" title="MINTO">MINTO</a><sup>∗</sup></li> <li><a href="/wiki/MOSEK" title="MOSEK">MOSEK</a><sup>∗</sup></li> <li><a href="/wiki/Numerical_Algorithms_Group" class="mw-redirect" title="Numerical Algorithms Group">NAG</a></li> <li><a href="/wiki/SCIP_(optimization_software)" class="mw-redirect" title="SCIP (optimization software)">SCIP</a><sup>∗</sup></li> <li><a href="/wiki/SCIP_(optimization_software)#SCIP_Optimization_Suite" class="mw-redirect" title="SCIP (optimization software)">SoPlex</a></li> <li><a href="/wiki/Octeract_Engine" title="Octeract Engine">Octeract Engine</a><sup>∗</sup></li> <li><a href="/wiki/COIN-OR#SYMPHONY" title="COIN-OR">SYMPHONY</a><sup>∗</sup></li> <li><a href="/wiki/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="/wiki/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 class="mw-selflink selflink">APOPT</a><sup>∗</sup></li> <li><a href="/wiki/ANTIGONE" title="ANTIGONE">ANTIGONE</a><sup>∗</sup></li> <li><a href="/wiki/Artelys_Knitro" title="Artelys Knitro">Artelys Knitro</a><sup>∗</sup></li> <li><a href="/wiki/COIN-OR#CBC" title="COIN-OR">CBC</a><sup>∗</sup></li> <li><a href="/wiki/COIN-OR#CLP" title="COIN-OR">CLP</a></li> <li><a href="/wiki/CPLEX" title="CPLEX">CPLEX</a><sup>∗</sup></li> <li><a href="/wiki/FortMP" title="FortMP">FortMP</a><sup>∗</sup></li> <li><a href="/wiki/HiGHS_optimization_solver" title="HiGHS optimization solver">HiGHS</a></li> <li><a href="/wiki/Gurobi_Optimizer" title="Gurobi Optimizer">Gurobi Optimizer</a><sup>∗</sup></li> <li><a href="/wiki/IPOPT" title="IPOPT">IPOPT</a></li> <li><a href="/wiki/LINDO" title="LINDO">LINDO</a><sup>∗</sup></li> <li><a href="/wiki/Mathematica" class="mw-redirect" title="Mathematica">Mathematica</a></li> <li><a href="/wiki/MINOS_(optimization_software)" title="MINOS (optimization software)">MINOS</a></li> <li><a href="/wiki/MOSEK" title="MOSEK">MOSEK</a><sup>∗</sup></li> <li><a href="/wiki/Numerical_Algorithms_Group" class="mw-redirect" title="Numerical Algorithms Group">NAG</a></li> <li><a href="/wiki/Octeract_Engine" title="Octeract Engine">Octeract Engine</a><sup>∗</sup></li> <li><a href="/wiki/SCIP_(optimization_software)" class="mw-redirect" title="SCIP (optimization software)">SCIP</a><sup>∗</sup></li> <li><a href="/wiki/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="/wiki/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 class="mw-selflink selflink">APOPT</a><sup>∗</sup></li> <li><a href="/wiki/ANTIGONE" title="ANTIGONE">ANTIGONE</a><sup>∗</sup></li> <li><a href="/wiki/Artelys_Knitro" title="Artelys Knitro">Artelys Knitro</a><sup>∗</sup></li> <li><a href="/wiki/CPLEX" title="CPLEX">CPLEX</a><sup>∗</sup></li> <li><a href="/wiki/Gurobi_Optimizer" title="Gurobi Optimizer">Gurobi Optimizer</a><sup>∗</sup></li> <li><a href="/wiki/IPOPT" title="IPOPT">IPOPT</a></li> <li><a href="/wiki/LINDO" title="LINDO">LINDO</a><sup>∗</sup></li> <li><a href="/wiki/Mathematica" class="mw-redirect" title="Mathematica">Mathematica</a></li> <li><a href="/wiki/MINOS_(optimization_software)" title="MINOS (optimization software)">MINOS</a></li> <li><a href="/wiki/MOSEK" title="MOSEK">MOSEK</a><sup>∗</sup></li> <li><a href="/wiki/Numerical_Algorithms_Group" class="mw-redirect" title="Numerical Algorithms Group">NAG</a></li> <li><a href="/wiki/SCIP_(optimization_software)" class="mw-redirect" title="SCIP (optimization software)">SCIP</a><sup>∗</sup></li> <li><a href="/wiki/Octeract_Engine" title="Octeract Engine">Octeract Engine</a><sup>∗</sup></li> <li><a href="/wiki/FICO_Xpress" title="FICO Xpress">Xpress Optimizer</a><sup>∗</sup></li> <li><a href="/wiki/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="/wiki/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="/wiki/Artelys_Knitro" title="Artelys Knitro">Artelys Knitro</a><sup>∗</sup></li> <li><a href="/wiki/CPLEX" title="CPLEX">CPLEX</a><sup>∗</sup></li> <li><a href="/wiki/Gurobi_Optimizer" title="Gurobi Optimizer">Gurobi Optimizer</a><sup>∗</sup></li> <li><a href="/wiki/LINDO" title="LINDO">LINDO</a><sup>∗</sup></li> <li><a href="/wiki/Robert_J._Vanderbei" title="Robert J. Vanderbei">LOQO</a></li> <li><a href="/wiki/Mathematica" class="mw-redirect" title="Mathematica">Mathematica</a></li> <li><a href="/wiki/MOSEK" title="MOSEK">MOSEK</a><sup>∗</sup></li> <li><a href="/wiki/Numerical_Algorithms_Group" class="mw-redirect" title="Numerical Algorithms Group">NAG</a></li> <li><a href="/wiki/SCIP_(optimization_software)" class="mw-redirect" title="SCIP (optimization software)">SCIP</a><sup>∗</sup></li> <li><a href="/wiki/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="/wiki/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="/wiki/Mathematica" class="mw-redirect" title="Mathematica">Mathematica</a></li> <li><a href="/wiki/MOSEK" title="MOSEK">MOSEK</a></li> <li><a href="/wiki/Numerical_Algorithms_Group" class="mw-redirect" title="Numerical Algorithms Group">NAG</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/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"> <ul><li><a href="/wiki/AIMMS_Outer_Approximation_(optimization_software)" class="mw-redirect" title="AIMMS Outer Approximation (optimization software)">AOA</a><sup>∗</sup></li> <li><a class="mw-selflink selflink">APOPT</a><sup>∗</sup></li> <li><a href="/wiki/ANTIGONE" title="ANTIGONE">ANTIGONE</a><sup>∗</sup></li> <li><a href="/wiki/Artelys_Knitro" title="Artelys Knitro">Artelys Knitro</a><sup>∗</sup></li> <li><a href="/wiki/BARON" title="BARON">BARON</a><sup>∗</sup></li> <li><a href="/wiki/Couenne" title="Couenne">Couenne</a><sup>∗</sup></li> <li><a href="/wiki/Galahad_library" title="Galahad library">Galahad library</a></li> <li><a href="/wiki/Gurobi_Optimizer" title="Gurobi Optimizer">Gurobi Optimizer</a><sup>∗</sup></li> <li><a href="/wiki/IPOPT" title="IPOPT">IPOPT</a></li> <li><a href="/wiki/LINDO" title="LINDO">LINDO</a><sup>∗</sup></li> <li><a href="/wiki/Robert_J._Vanderbei" title="Robert J. Vanderbei">LOQO</a></li> <li><a href="/wiki/MIDACO" title="MIDACO">MIDACO</a><sup>∗</sup></li> <li><a href="/wiki/MINOS_(optimization_software)" title="MINOS (optimization software)">MINOS</a></li> <li><a href="/wiki/Numerical_Algorithms_Group" class="mw-redirect" title="Numerical Algorithms Group">NAG</a></li> <li><a href="/wiki/NLPQLP" title="NLPQLP">NLPQLP</a></li> <li><a href="/wiki/NPSOL" title="NPSOL">NPSOL</a></li> <li><a href="/wiki/SCIP_(optimization_software)" class="mw-redirect" title="SCIP (optimization software)">SCIP</a><sup>∗</sup></li> <li><a href="/wiki/SNOPT" title="SNOPT">SNOPT</a><sup>∗</sup></li> <li><a href="/wiki/Octeract_Engine" title="Octeract Engine">Octeract Engine</a><sup>∗</sup></li> <li><a href="/wiki/WORHP" title="WORHP">WORHP</a></li> <li><a href="/wiki/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="/wiki/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="/wiki/ANTIGONE" title="ANTIGONE">ANTIGONE</a><sup>∗</sup></li> <li><a href="/wiki/BARON" title="BARON">BARON</a></li> <li><a href="/wiki/Couenne" title="Couenne">Couenne</a><sup>∗</sup></li> <li><a href="/wiki/FICO_Xpress" title="FICO Xpress">Xpress Global</a></li> <li><a href="/wiki/Mathematica" class="mw-redirect" title="Mathematica">Mathematica</a></li> <li><a href="/wiki/LINDO" title="LINDO">LINDO</a></li> <li><a href="/wiki/SCIP_(optimization_software)" class="mw-redirect" title="SCIP (optimization software)">SCIP</a></li> <li><a href="/wiki/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="/wiki/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="/wiki/CPLEX" title="CPLEX">CPLEX</a> CP Optimizer</li> <li><a href="/wiki/Gecode" title="Gecode">Gecode</a></li> <li><a href="/wiki/Mathematica" class="mw-redirect" title="Mathematica">Mathematica</a></li> <li><a href="/wiki/JaCoP_(solver)" title="JaCoP (solver)">JaCoP</a></li> <li><a href="/wiki/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="/wiki/List_of_optimization_software" title="List of optimization software">List of optimization software</a></b></li> <li><b><a href="/wiki/Comparison_of_optimization_software" title="Comparison of optimization software">Comparison of optimization software</a></b></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=APOPT&oldid=1265318166">https://en.wikipedia.org/w/index.php?title=APOPT&oldid=1265318166</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Numerical_software" title="Category:Numerical software">Numerical software</a></li><li><a href="/wiki/Category:Mathematical_optimization_software" title="Category:Mathematical optimization software">Mathematical optimization software</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden category: <ul><li><a href="/wiki/Category:Official_website_different_in_Wikidata_and_Wikipedia" title="Category:Official website different in Wikidata and Wikipedia">Official website different in Wikidata and Wikipedia</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 26 December 2024, at 09:15<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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vector-button-flush-left" > <input type="checkbox" id="vector-sticky-header-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-sticky-header-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-sticky-header-toc-label" for="vector-sticky-header-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-sticky-header-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div class="vector-sticky-header-context-bar-primary" aria-hidden="true" ><span class="mw-page-title-main">APOPT</span></div> </div> </div> <div class="vector-sticky-header-end" aria-hidden="true"> <div class="vector-sticky-header-icons"> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-talk-sticky-header" tabindex="-1" data-event-name="talk-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbles mw-ui-icon-wikimedia-speechBubbles"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-subject-sticky-header" tabindex="-1" data-event-name="subject-sticky-header"><span class="vector-icon mw-ui-icon-article mw-ui-icon-wikimedia-article"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-history-sticky-header" tabindex="-1" data-event-name="history-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-history mw-ui-icon-wikimedia-wikimedia-history"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only mw-watchlink" id="ca-watchstar-sticky-header" tabindex="-1" data-event-name="watch-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-star mw-ui-icon-wikimedia-wikimedia-star"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-edit-sticky-header" tabindex="-1" data-event-name="wikitext-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-wikiText mw-ui-icon-wikimedia-wikimedia-wikiText"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-ve-edit-sticky-header" tabindex="-1" data-event-name="ve-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-edit mw-ui-icon-wikimedia-wikimedia-edit"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-viewsource-sticky-header" tabindex="-1" data-event-name="ve-edit-protected-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-editLock mw-ui-icon-wikimedia-wikimedia-editLock"></span> <span></span> </a> </div> <div class="vector-sticky-header-buttons"> <button class="cdx-button cdx-button--weight-quiet mw-interlanguage-selector" id="p-lang-btn-sticky-header" tabindex="-1" data-event-name="ui.dropdown-p-lang-btn-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-language mw-ui-icon-wikimedia-wikimedia-language"></span> <span>Add languages</span> </button> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive" id="ca-addsection-sticky-header" tabindex="-1" data-event-name="addsection-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbleAdd-progressive mw-ui-icon-wikimedia-speechBubbleAdd-progressive"></span> <span>Add topic</span> </a> </div> <div class="vector-sticky-header-icon-end"> <div class="vector-user-links"> </div> </div> </div> </div> </div> <div class="mw-portlet mw-portlet-dock-bottom emptyPortlet" id="p-dock-bottom"> <ul> </ul> </div> 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