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The AMPL Modeling Language: An Aid to Formulating and Solving Optimization Problems

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Numerical Analysis and Optimization

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 134))

Abstract

Optimization problems arise in many contexts. Sometimes finding a good formulation takes considerable effort. A modeling language, such as AMPL, facilitates experimenting with formulations and simplifies using suitable solvers to solve the resulting optimization problems. AMPL lets one use notation close to familiar mathematical notation to state variables, objectives, and constraints and the sets and parameters that may be involved. AMPL does some problem transformations and makes relevant problem information available to solvers. The AMPL command language permits computing and displaying information about problem details and solutions returned by solvers. It also lets one modify problem formulations and solve sequences of problems. AMPL addresses both continuous and discrete optimization problems and offers some constraint-programming facilities for the latter. More generally, AMPL permits stating and solving problems with complementarity constraints. For continuous problems, AMPL makes first and second derivatives available via automatic differentiation. The freely available AMPL/solver interface library (ASL) facilitates interfacing with solvers. This paper gives an overview of AMPL and its interaction with solvers and discusses some problem transformations and implementation techniques. It also looks forward to possible enhancements to AMPL.

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Author information

Authors and Affiliations

  1. AMPL Optimization Inc., 900 Sierra Place SE, Albuquerque, NM, 87108-3379, USA

    David M. Gay

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  1. David M. Gay
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Correspondence to David M. Gay .

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Editors and Affiliations

  1. Department of Mathematics College of Science, Sultan Qaboos University, Muscat, Oman

    Mehiddin Al-Baali

  2. Faculty of Engineering, University of Calabria, Arcavacada di Rende, Italy

    Lucio Grandinetti

  3. Department Mathematics and Statistics College of Science, Sultan Qaboos University, Muscat, Oman

    Anton Purnama

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Gay, D.M. (2015). The AMPL Modeling Language: An Aid to Formulating and Solving Optimization Problems. In: Al-Baali, M., Grandinetti, L., Purnama, A. (eds) Numerical Analysis and Optimization. Springer Proceedings in Mathematics & Statistics, vol 134. Springer, Cham. https://doi.org/10.1007/978-3-319-17689-5_5

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