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MathOptInterface: A Data Structure for Mathematical Optimization Problems

Author

Listed:
  • Benoît Legat

    (Institute for Information and Communication Technologies, Electronics and Applied Mathematics, Université Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium)

  • Oscar Dowson

    (Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208)

  • Joaquim Dias Garcia

    (PSR, 22250-040 Rio de Janeiro-RJ, Brazil; Pontifícia Universidade Católica do Rio de Janeiro, 22451-900 Rio de Janeiro-RJ, Brazil)

  • Miles Lubin

    (Google Research, New York, New York 10011)

Abstract

We introduce MathOptInterface, an abstract data structure for representing mathematical optimization problems based on combining predefined functions and sets. MathOptInterface is significantly more general than existing data structures in the literature, encompassing, for example, a spectrum of problems classes from integer programming with indicator constraints to bilinear semidefinite programming. We also outline an automated rewriting system between equivalent formulations of a constraint. MathOptInterface has been implemented in practice, forming the foundation of a recent rewrite of JuMP, an open-source algebraic modeling language in the Julia language. The regularity of the MathOptInterface representation leads naturally to a general file format for mathematical optimization we call MathOptFormat . In addition, the automated rewriting system provides modeling power to users while making it easy to connect new solvers to JuMP. Summary of Contribution: This paper describes a new abstract data structure for representing mathematical optimization models with a corresponding file format and automatic transformation system. The advances are useful for algebraic modeling languages, allowing practitioners to model problems more naturally and more generally than before.

Suggested Citation

  • Benoît Legat & Oscar Dowson & Joaquim Dias Garcia & Miles Lubin, 2022. "MathOptInterface: A Data Structure for Mathematical Optimization Problems," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 672-689, March.
    • Handle: RePEc:inm:orijoc:v:34:y:2022:i:2:p:672-689
    DOI: 10.1287/ijoc.2021.1067
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    References listed on IDEAS

    as
    1. Robert Fourer & Jun Ma & Kipp Martin, 2010. "OSiL: An instance language for optimization," Computational Optimization and Applications, Springer, vol. 45(1), pages 181-203, January.
    2. Brendan O’Donoghue & Eric Chu & Neal Parikh & Stephen Boyd, 2016. "Conic Optimization via Operator Splitting and Homogeneous Self-Dual Embedding," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 1042-1068, June.
    3. Robert Fourer & David M. Gay & Brian W. Kernighan, 1990. "A Modeling Language for Mathematical Programming," Management Science, INFORMS, vol. 36(5), pages 519-554, May.
    4. Miles Lubin & Iain Dunning, 2015. "Computing in Operations Research Using Julia," INFORMS Journal on Computing, INFORMS, vol. 27(2), pages 238-248, May.
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    Cited by:

    1. Mathieu Besançon & Miguel F. Anjos & Luce Brotcorne, 2024. "Robust bilevel optimization for near-optimal lower-level solutions," Journal of Global Optimization, Springer, vol. 90(4), pages 813-842, December.
    2. Mathieu Besançon & Joaquim Dias Garcia & Benoît Legat & Akshay Sharma, 2024. "Flexible Differentiable Optimization via Model Transformations," INFORMS Journal on Computing, INFORMS, vol. 36(2), pages 456-478, March.
    3. Joaquim Dias Garcia & Guilherme Bodin & Alexandre Street, 2024. "BilevelJuMP.jl: Modeling and Solving Bilevel Optimization Problems in Julia," INFORMS Journal on Computing, INFORMS, vol. 36(2), pages 327-335, March.
    4. Chris Coey & Lea Kapelevich & Juan Pablo Vielma, 2022. "Solving Natural Conic Formulations with Hypatia.jl," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2686-2699, September.

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