AMPL

<h2 id="features">Features</h2>
AMPL features a mix of <a href="/facts/Declarative_programming/gogtdzcJ">declarative</a> and <a href="/facts/Imperative_programming/6b5dUnE1">imperative</a> programming styles. Formulating optimization models occurs via declarative language elements such as sets, scalar and multidimensional parameters, decision variables, objectives and <a href="/facts/Constraint_(mathematics)/QLFIFlFX">constraints</a>, which allow for concise description of most problems in the domain of mathematical optimization.
Procedures and <a href="/facts/Control_flow/2XTDfErC">control flow</a> statements are available in AMPL for

<ul><li>the exchange of data with external data sources such as <a href="/facts/Spreadsheet/0cvc1GeB">spreadsheets</a>, <a href="/facts/Database/VYcpkevb">databases</a>, <a href="/facts/XML/clNgUfWk">XML</a> and text files</li>
<li>data pre- and post-processing tasks around optimization models</li>
<li>the construction of hybrid algorithms for problem types for which no direct efficient solvers are available.</li></ul>
To support re-use and simplify construction of large-scale optimization problems, AMPL allows separation of model and data.
AMPL supports a wide range of problem types, among them:

<ul><li><a href="/facts/Linear_programming/GduXFQxT">Linear programming</a></li>
<li><a href="/facts/Quadratic_programming/ct4RIUgs">Quadratic programming</a></li>
<li><a href="/facts/Nonlinear_programming/cSXGuX2m">Nonlinear programming</a></li>
<li><a href="/facts/Linear_programming/GduXFQxT">Mixed-integer programming</a></li>
<li>Mixed-integer quadratic programming with or without <a href="/facts/Convex_function/IbzG5SLF">convex</a> quadratic constraints</li>
<li>Mixed-integer nonlinear programming</li>
<li><a href="/facts/Second-order_cone_programming/TNXLKvK7">Second-order cone programming</a></li>
<li><a href="/facts/Global_optimization/nksWlDqU">Global optimization</a></li>
<li><a href="/facts/Semidefinite_programming/pFN25EKE">Semidefinite programming</a> problems with <a href="/facts/Bilinear_form/gyvzn9ym">bilinear</a> matrix inequalities</li>
<li><a href="/facts/Complementarity_theory/WYSSukXu">Complementarity theory</a> problems (MPECs) in discrete or continuous variables</li>
<li><a href="/facts/Constraint_programming/rgkCK5bD">Constraint programming</a><a class="footnote-ref" id="fnref:4" href="#fn:4">4</a></li></ul>
AMPL invokes a solver in a separate process which has these advantages:

<ul><li>User can interrupt the solution process at any time</li>
<li>Solver errors do not affect the interpreter</li>
<li>32-bit version of AMPL can be used with a 64-bit solver and vice versa</li></ul>
Interaction with the solver is done through a well-defined <a href="/facts/Nl_(format)/9U0EyckP">nl interface</a>.

<h2 id="availability">Availability</h2>
AMPL is available for many popular 32 & 64-bit <a href="/facts/Operating_system/8XTuvMh2">operating systems</a> including <a href="/facts/Linux/9FvCKSTq">Linux</a>, <a href="/facts/MacOS/Y93vVpTm">macOS</a>, <a href="/facts/Solaris_(operating_system)/KPfT98EJ">Solaris</a>, <a href="/facts/IBM_AIX/cRWERua2">AIX</a>, and <a href="/facts/Microsoft_Windows/bwhAhuSL">Windows</a>.<a class="footnote-ref" id="fnref:5" href="#fn:5">5</a>
The translator is proprietary software maintained by AMPL Optimization LLC. However, several online services exist, providing free modeling and solving facilities using AMPL.<a class="footnote-ref" id="fnref:6" href="#fn:6">6</a><a class="footnote-ref" id="fnref:7" href="#fn:7">7</a> A free student version with limited functionality and a free full-featured version for academic courses are also available.<a class="footnote-ref" id="fnref:8" href="#fn:8">8</a>
AMPL can be used from within <a href="/facts/Microsoft_Excel/Ezal6G75">Microsoft Excel</a> via the <a href="/facts/SolverStudio/h6mEFjDb">SolverStudio</a> Excel add-in.
The AMPL Solver Library (ASL), which allows reading nl files and provides the automatic differentiation, is open-source. It is used in many solvers to implement AMPL connection.

<h2 id="status-history">Status history</h2>
This table present significant steps in AMPL history.

<table><tbody><tr><th>Year</th><th>Highlights</th></tr><tr><td>1985</td><td>AMPL was designed and implemented<a class="footnote-ref" id="fnref:9" href="#fn:9">9</a></td></tr><tr><td>1990</td><td>Paper describing the AMPL modeling language was published in <a href="/facts/Management_Science%3a_A_Journal_of_the_Institute_for_Operations_Research_and_the_Management_Sciences/vsIxkCsL">Management Science</a><a class="footnote-ref" id="fnref:10" href="#fn:10">10</a></td></tr><tr><td>1991</td><td>AMPL supports <a href="/facts/Nonlinear_programming/cSXGuX2m">nonlinear programming</a> and <a href="/facts/Automatic_differentiation/dQcdhBAM">automatic differentiation</a></td></tr><tr><td>1993</td><td><a href="/facts/Robert_Fourer/kK9usl1o">Robert Fourer</a>, David Gay and <a href="/facts/Brian_Kernighan/oW3I7FWJ">Brian Kernighan</a> were awarded ORSA/CSTS Prize<a class="footnote-ref" id="fnref:11" href="#fn:11">11</a> by the <a href="/facts/Operations_Research_Society_of_America/pALUR8e3">Operations Research Society of America</a>, for writings on the design of mathematical programming systems and the AMPL modeling language</td></tr><tr><td>1995</td><td>Extensions for representing <a href="/facts/Piecewise_linear_function/6bKlCbEa">piecewise-linear</a> and network structures</td></tr><tr><td>1995</td><td>Scripting constructs</td></tr><tr><td>1997</td><td>Enhanced support for nonlinear solvers</td></tr><tr><td>1998</td><td>AMPL supports <a href="/facts/Complementarity_theory/WYSSukXu">complementarity theory</a> problems</td></tr><tr><td>2000</td><td>Relational database and spreadsheet access</td></tr><tr><td>2002</td><td>Support for constraint programming<a class="footnote-ref" id="fnref:12" href="#fn:12">12</a></td></tr><tr><td>2003</td><td>AMPL Optimization LLC was founded by the inventors of AMPL, Robert Fourer, David Gay, and Brian Kernighan. The new company took over the development and support of the AMPL modeling language from <a href="/facts/Lucent/uzgpVmLa">Lucent Technologies, Inc</a>.</td></tr><tr><td>2005</td><td>AMPL Modeling Language Google group opened<a class="footnote-ref" id="fnref:13" href="#fn:13">13</a></td></tr><tr><td>2008</td><td>Kestrel: An AMPL Interface to the NEOS Server introduced</td></tr><tr><td>2012</td><td><a href="/facts/Robert_Fourer/kK9usl1o">Robert Fourer</a>, David Gay, and <a href="/facts/Brian_Kernighan/oW3I7FWJ">Brian Kernighan</a> were awarded the 2012 INFORMS Impact Prize as the originators of one of the most important algebraic modeling languages.<a class="footnote-ref" id="fnref:14" href="#fn:14">14</a></td></tr><tr><td>2012</td><td>AMPL book becomes freely available online<a class="footnote-ref" id="fnref:15" href="#fn:15">15</a></td></tr><tr><td>2013</td><td>A new cross-platform <a href="/facts/Integrated_development_environment/jbEINSQf">integrated development environment</a> (IDE) for AMPL becomes available<a class="footnote-ref" id="fnref:16" href="#fn:16">16</a></td></tr></tbody></table>
<h2 id="a-sample-model">A sample model</h2>
A transportation problem from <a href="/facts/George_Dantzig/04se7h0M">George Dantzig</a> is used to provide a sample AMPL model. This problem finds the least cost shipping schedule that meets requirements at markets and supplies at factories.<a class="footnote-ref" id="fnref:17" href="#fn:17">17</a>

 set Plants;
 set Markets;

# Capacity of plant p in cases
 param Capacity{p in Plants};

# Demand at market m in cases
 param Demand{m in Markets};

# Distance in thousands of miles
 param Distance{Plants, Markets};

# Freight in dollars per case per thousand miles
 param Freight;

# Transport cost in thousands of dollars per case
 param TransportCost{p in Plants, m in Markets} :=
     Freight * Distance[p, m] / 1000;

# Shipment quantities in cases
 var shipment{Plants, Markets} >= 0;

# Total transportation costs in thousands of dollars
 minimize cost:
     sum{p in Plants, m in Markets} TransportCost[p, m] * shipment[p, m];

# Observe supply limit at plant p
 s.t. supply{p in Plants}: sum{m in Markets} shipment[p, m] <= Capacity[p];

# Satisfy demand at market m
 s.t. demand{m in Markets}: sum{p in Plants} shipment[p, m] >= Demand[m];

data;

set Plants := seattle san-diego;
 set Markets := new-york chicago topeka;

param Capacity :=
     seattle   350
     san-diego 600;

param Demand :=
     new-york 325
     chicago  300
     topeka   275;

param Distance : new-york chicago topeka :=
     seattle        2.5      1.7     1.8
     san-diego      2.5      1.8     1.4;

param Freight := 90;

<h2 id="solvers">Solvers</h2>
Here is a partial list of <a href="/facts/Solver/S8LurhlM">solvers</a> supported by AMPL:<a class="footnote-ref" id="fnref:18" href="#fn:18">18</a>

<table><tbody><tr><th>Solver</th><th>Supported problem types</th></tr><tr><th><a href="/facts/APOPT/uwFQSmAL">APOPT</a></th><td>mixed integer <a href="/facts/Nonlinear_programming/cSXGuX2m">nonlinear programming</a></td></tr><tr><th><a href="/facts/Artelys_Knitro/e5D2EHkH">Artelys Knitro</a></th><td>linear, quadratic and nonlinear programming</td></tr><tr><th>Bonmin</th><td>mixed integer <a href="/facts/Nonlinear_programming/cSXGuX2m">nonlinear programming</a></td></tr><tr><th>BPMPD</th><td><a href="/facts/Linear_programming/GduXFQxT">linear</a> and <a href="/facts/Quadratic_programming/ct4RIUgs">quadratic programming</a></td></tr><tr><th><a href="/facts/COIN-OR/we1fYPNj">COIN-OR</a> CBC</th><td><a href="/facts/Linear_programming/GduXFQxT">mixed integer programming</a></td></tr><tr><th><a href="/facts/COIN-OR/we1fYPNj">COIN-OR CLP</a></th><td>linear programming</td></tr><tr><th>CONOPT</th><td>nonlinear programming</td></tr><tr><th><a href="/facts/Couenne/faf042MX">Couenne</a><a class="footnote-ref" id="fnref:19" href="#fn:19">19</a></th><td>mixed integer nonlinear programming (MINLP)</td></tr><tr><th><a href="/facts/CPLEX/SnfwWLtb">CPLEX</a></th><td>linear, quadratic, <a href="/facts/Second-order_cone_programming/TNXLKvK7">second-order cone</a> and mixed integer programming</td></tr><tr><th>CPLEX CP Optimizer<a class="footnote-ref" id="fnref:20" href="#fn:20">20</a></th><td><a href="/facts/Constraint_programming/rgkCK5bD">constraint programming</a></td></tr><tr><th>FILTER</th><td>nonlinear programming</td></tr><tr><th><a href="/facts/FortMP/IFu9YFxa">FortMP</a></th><td>linear, quadratic and mixed integer programming</td></tr><tr><th><a href="/facts/Gecode/fRYly5fM">Gecode</a><a class="footnote-ref" id="fnref:21" href="#fn:21">21</a></th><td>constraint programming</td></tr><tr><th><a href="/facts/IPOPT/EdoDsb0Y">IPOPT</a></th><td>nonlinear programming</td></tr><tr><th><a href="/facts/JaCoP_(solver)/uhKtVCaV">JaCoP</a><a class="footnote-ref" id="fnref:22" href="#fn:22">22</a></th><td>constraint programming</td></tr><tr><th>LGO<a class="footnote-ref" id="fnref:23" href="#fn:23">23</a></th><td>global and local nonlinear optimization</td></tr><tr><th>lp_solve<a class="footnote-ref" id="fnref:24" href="#fn:24">24</a></th><td>linear and mixed integer programming</td></tr><tr><th><a href="/facts/MINOS_(optimization_software)/MVBW3g9S">MINOS</a></th><td>linear and nonlinear programming</td></tr><tr><th><a href="/facts/MINTO/QV0APjnG">MINTO</a></th><td>mixed integer programming</td></tr><tr><th><a href="/facts/MOSEK/zfmWsyqy">MOSEK</a></th><td>linear, mixed integer linear, quadratic, mixed integer quadratic, <a href="/facts/Quadratically_constrained_quadratic_program/H518KTl3">quadratically constrained</a>, conic and convex nonlinear programming</td></tr><tr><th><a href="/facts/Octeract_Engine/kw1S3sgc">Octeract Engine</a></th><td>All types of optimisation problems without differential or integral terms, including discontinuous problems with min and max elementary functions.</td></tr><tr><th><a href="/facts/SCIP_(optimization_software)/3ovWAS4b">SCIP</a></th><td>mixed integer programming</td></tr><tr><th><a href="/facts/SNOPT/Jg7Xrr6d">SNOPT</a></th><td>nonlinear programming</td></tr><tr><th>Sulum<a class="footnote-ref" id="fnref:25" href="#fn:25">25</a></th><td>linear and mixed integer programming</td></tr><tr><th><a href="/facts/WORHP/MLKA94rw">WORHP</a></th><td>nonlinear programming</td></tr><tr><th>XA</th><td>linear and mixed integer programming</td></tr><tr><th><a href="/facts/FICO_Xpress/mEFKqwEG">Xpress</a></th><td>linear and convex <a href="/facts/Quadratically_constrained_quadratic_program/H518KTl3">quadratic optimization</a> and their mixed integer counterparts</td></tr></tbody></table>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Sol_(format)/BpIGCCvr">sol (format)</a></li>
<li><a href="/facts/GNU_MathProg/9j7hhN95">GNU MathProg</a> (previously known as GMPL) is a subset of AMPL supported by the <a href="/facts/GNU_Linear_Programming_Kit/9j7hhN95">GNU Linear Programming Kit</a><a class="footnote-ref" id="fnref:26" href="#fn:26">26</a></li></ul>

<h2 id="external-links">External links</h2>
<ul><li><a href="http://www.ampl.com">Official website</a></li>
<li><a href="https://web.archive.org/web/20061127232734/http://iems.northwestern.edu/~4er/">Prof. Fourer's home page</a> at <a href="/facts/Northwestern_University/4dunJHBf">Northwestern University</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1">Fourer, Robert; Gay, David M; Kernighan, Brian W (2003). AMPL: a modeling language for mathematical programming. USA: Duxbury Press/Brooks/Cole Publishing Company. ISBN 978-0-534-38809-6. <a href="978-0-534-38809-6" target="_blank">978-0-534-38809-6</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></li>
<li id="fn:2">"Position Available". Archived from the original on 11 September 2011. Retrieved 29 July 2011. <a href="https://web.archive.org/web/20110911191129/http://www.ampl.com/OPENINGS/2011July.html#Product" target="_blank">https://web.archive.org/web/20110911191129/http://www.ampl.com/OPENINGS/2011July.html#Product</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></li>
<li id="fn:3">"About". Retrieved 11 August 2015. <a href="http://neos-guide.org/About/" target="_blank">http://neos-guide.org/About/</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></li>
<li id="fn:4">Fourer, Robert; Gay, David M. (2002). "Extending an Algebraic Modeling Language to Support Constraint Programming". INFORMS Journal on Computing. 14 (4): 322–344. CiteSeerX 10.1.1.8.9699. doi:10.1287/ijoc.14.4.322.2825. <a href="/wiki/Robert_Fourer" target="_blank">/wiki/Robert_Fourer</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></li>
<li id="fn:5">"Platforms". AMPL Optimizations Inc. Archived from the original on 14 May 2022. Retrieved 1 November 2019. <a href="https://web.archive.org/web/20220514181833/https://ampl.com/products/platforms/" target="_blank">https://web.archive.org/web/20220514181833/https://ampl.com/products/platforms/</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></li>
<li id="fn:6">"NEOS Server for Optimization". Retrieved 11 August 2015. <a href="http://www.neos-server.org/neos/" target="_blank">http://www.neos-server.org/neos/</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></li>
<li id="fn:7">"Try AMPL!". Retrieved 11 August 2015. <a href="http://www.ampl.com/TRYAMPL/" target="_blank">http://www.ampl.com/TRYAMPL/</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></li>
<li id="fn:8">"AMPL Downloads". Archived from the original on 26 May 2015. Retrieved 11 August 2015. <a href="https://web.archive.org/web/20150526013237/http://www.ampl.com/DOWNLOADS/index.html" target="_blank">https://web.archive.org/web/20150526013237/http://www.ampl.com/DOWNLOADS/index.html</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></li>
<li id="fn:9">Fourer, Robert; Gay, David M; Kernighan, Brian W (2003). AMPL: a modeling language for mathematical programming. USA: Duxbury Press/Brooks/Cole Publishing Company. ISBN 978-0-534-38809-6. <a href="978-0-534-38809-6" target="_blank">978-0-534-38809-6</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></li>
<li id="fn:10">Fourer, Robert; Gay, David M.; Kernighan, Brian W. (1990). "A Modeling Language for Mathematical Programming" (PDF). Management Science. 36 (5): 519–554–83. doi:10.1287/mnsc.36.5.519. <a href="/wiki/Robert_Fourer" target="_blank">/wiki/Robert_Fourer</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></li>
<li id="fn:11">INFORMS. "ICS - INFORMS" (PDF). Archived from the original (PDF) on 7 October 2006. Retrieved 11 August 2015. <a href="https://web.archive.org/web/20061007164141/http://computing.society.informs.org/pdf/GreenbergHistory.pdf" target="_blank">https://web.archive.org/web/20061007164141/http://computing.society.informs.org/pdf/GreenbergHistory.pdf</a> <a href="#fnref:11" class="footnote-back-ref">↩</a></li>
<li id="fn:12">Fourer, Robert; Gay, David M. (2002). "Extending an Algebraic Modeling Language to Support Constraint Programming". INFORMS Journal on Computing. 14 (4): 322–344. CiteSeerX 10.1.1.8.9699. doi:10.1287/ijoc.14.4.322.2825. <a href="/wiki/Robert_Fourer" target="_blank">/wiki/Robert_Fourer</a> <a href="#fnref:12" class="footnote-back-ref">↩</a></li>
<li id="fn:13">"Google Groups". <a href="https://groups.google.com/group/ampl" target="_blank">https://groups.google.com/group/ampl</a> <a href="#fnref:13" class="footnote-back-ref">↩</a></li>
<li id="fn:14">INFORMS. "INFORMS Impact Prize". Archived from the original on 22 October 2013. Retrieved 11 August 2015. <a href="https://web.archive.org/web/20131022091250/https://www.informs.org/Blogs/E-News-Blog/INFORMS-Impact-Prize" target="_blank">https://web.archive.org/web/20131022091250/https://www.informs.org/Blogs/E-News-Blog/INFORMS-Impact-Prize</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></li>
<li id="fn:15">"The AMPL Book: A comprehensive guide to building optimization models, for beginning or experienced users". Retrieved 5 March 2021. <a href="https://ampl.com/learn/ampl-book/" target="_blank">https://ampl.com/learn/ampl-book/</a> <a href="#fnref:15" class="footnote-back-ref">↩</a></li>
<li id="fn:16">"Google Groups". Retrieved 11 August 2015. <a href="https://groups.google.com/forum/#!topic/ampl/y1FJcYZz-_Q" target="_blank">https://groups.google.com/forum/#!topic/ampl/y1FJcYZz-_Q</a> <a href="#fnref:16" class="footnote-back-ref">↩</a></li>
<li id="fn:17">Dantzig, George (2016) [1963]. "3. Formulating a Linear Programming Model". Linear Programming and Extensions. Princeton University Press. pp. 32–62. ISBN 978-1-4008-8417-9. <a href="978-1-4008-8417-9" target="_blank">978-1-4008-8417-9</a> <a href="#fnref:17" class="footnote-back-ref">↩</a></li>
<li id="fn:18">"Solvers - AMPL". Archived from the original on 27 February 2014. Retrieved 21 January 2018. <a href="https://web.archive.org/web/20140227083015/http://www.ampl.com/solvers.html" target="_blank">https://web.archive.org/web/20140227083015/http://www.ampl.com/solvers.html</a> <a href="#fnref:18" class="footnote-back-ref">↩</a></li>
<li id="fn:19">"Couenne". Archived from the original on 29 October 2013. Retrieved 27 October 2013. <a href="https://web.archive.org/web/20131029190415/https://projects.coin-or.org/Couenne" target="_blank">https://web.archive.org/web/20131029190415/https://projects.coin-or.org/Couenne</a> <a href="#fnref:19" class="footnote-back-ref">↩</a></li>
<li id="fn:20">"mp/solvers/ilogcp at master · ampl/mp · GitHub". GitHub. Retrieved 11 August 2015. <a href="https://github.com/ampl/mp/tree/master/solvers/ilogcp" target="_blank">https://github.com/ampl/mp/tree/master/solvers/ilogcp</a> <a href="#fnref:20" class="footnote-back-ref">↩</a></li>
<li id="fn:21">"mp/solvers/gecode at master · ampl/mp · GitHub". GitHub. Retrieved 11 August 2015. <a href="https://github.com/ampl/mp/tree/master/solvers/gecode" target="_blank">https://github.com/ampl/mp/tree/master/solvers/gecode</a> <a href="#fnref:21" class="footnote-back-ref">↩</a></li>
<li id="fn:22">"mp/solvers/jacop at master · ampl/mp · GitHub". GitHub. Retrieved 11 August 2015. <a href="https://github.com/ampl/mp/tree/master/solvers/jacop" target="_blank">https://github.com/ampl/mp/tree/master/solvers/jacop</a> <a href="#fnref:22" class="footnote-back-ref">↩</a></li>
<li id="fn:23">"LGO - AMPL". Retrieved 11 August 2015. <a href="http://ampl.com/products/solvers/solvers-we-sell/lgo/" target="_blank">http://ampl.com/products/solvers/solvers-we-sell/lgo/</a> <a href="#fnref:23" class="footnote-back-ref">↩</a></li>
<li id="fn:24">"Using lpsolve from AMPL". Retrieved 11 August 2015. <a href="http://www.ampl.com/SOLVERS/GUIDE.lpsolve.html" target="_blank">http://www.ampl.com/SOLVERS/GUIDE.lpsolve.html</a> <a href="#fnref:24" class="footnote-back-ref">↩</a></li>
<li id="fn:25">"mp/solvers/sulum at master · ampl/mp · GitHub". GitHub. Retrieved 11 August 2015. <a href="https://github.com/ampl/mp/tree/master/solvers/sulum" target="_blank">https://github.com/ampl/mp/tree/master/solvers/sulum</a> <a href="#fnref:25" class="footnote-back-ref">↩</a></li>
<li id="fn:26">"GLPK official site". Retrieved 17 September 2020. <a href="https://www.gnu.org/software/glpk/" target="_blank">https://www.gnu.org/software/glpk/</a> <a href="#fnref:26" class="footnote-back-ref">↩</a></li>
</ol>

AMPL open-in-new

AMPL