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International Symposium on Practical Aspects of Declarative Languages

PADL 2010: Practical Aspects of Declarative Languages pp 134–148Cite as

Automating Mathematical Program Transformations

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 5937))

Abstract

Mathematical programs (MPs) are a class of constrained optimization problems that include linear, mixed-integer, and disjunctive programs. Strategies for solving MPs rely heavily on various transformations between these subclasses, but most are not automated because MP theory does not presently treat programs as syntactic objects. In this work, we present the first syntactic definition of MP and of some widely used MP transformations, most notably the big-M and convex hull methods for converting disjunctive constraints. We use an embedded OCaml DSL on problems from chemical process engineering and operations research to compare our automated transformations to existing technology—finding that no one technique is always best—and also to manual reformulations—finding that our mechanizations are comparable to human experts. This work enables higher-level solution strategies that can use these transformations as subroutines.

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Author information

Authors and Affiliations

  1. Dept. of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA, 15213

    Ashish Agarwal & Ignacio E. Grossmann

  2. College of Computing, Georgia Institute of Technology, Atlanta, GA, 30332

    Sooraj Bhat & Alexander Gray

Authors
  1. Ashish Agarwal
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  2. Sooraj Bhat
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  3. Alexander Gray
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  4. Ignacio E. Grossmann
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Editor information

Editors and Affiliations

  1. Facultad de Informática, Univrsidad Politécnica de Madrid (UPM), Campus Montegancedo, Boadilla del Monte, 28660, Madrid, Spain

    Manuel Carro

  2. Facultad de Informática, Universidad Complutense de Madrid (UPM), c/Profesor José García Santesmases s/n, 28040, Madrid, Spain

    Ricardo Peña

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Agarwal, A., Bhat, S., Gray, A., Grossmann, I.E. (2010). Automating Mathematical Program Transformations. In: Carro, M., Peña, R. (eds) Practical Aspects of Declarative Languages. PADL 2010. Lecture Notes in Computer Science, vol 5937. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11503-5_12

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  • DOI: https://doi.org/10.1007/978-3-642-11503-5_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11502-8

  • Online ISBN: 978-3-642-11503-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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