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Flexible Differentiable Optimization via Model Transformations

Author

Listed:
  • Mathieu Besançon

    (Zuse Institute Berlin, Berlin 14195, Germany)

  • Joaquim Dias Garcia

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

  • Benoît Legat

    (KU Leuven, Department of Electrical Engineering (ESAT), STADIUS Center for Dynamical Systems, Signal Processing and Data Analytic, 3001 Leuven, Belgium)

  • Akshay Sharma

    (Columbia University, New York, New York 10027)

Abstract

We introduce DiffOpt.jl, a Julia library to differentiate through the solution of optimization problems with respect to arbitrary parameters present in the objective and/or constraints. The library builds upon MathOptInterface, thus leveraging the rich ecosystem of solvers and composing well with modeling languages like JuMP. DiffOpt offers both forward and reverse differentiation modes, enabling multiple use cases from hyperparameter optimization to backpropagation and sensitivity analysis, bridging constrained optimization with end-to-end differentiable programming. DiffOpt is built on two known rules for differentiating quadratic programming and conic programming standard forms. However, thanks to its ability to differentiate through model transformations, the user is not limited to these forms and can differentiate with respect to the parameters of any model that can be reformulated into these standard forms. This notably includes programs mixing affine conic constraints and convex quadratic constraints or objective function.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:orijoc:v:36:y:2024:i:2:p:456-478
    DOI: 10.1287/ijoc.2022.0283
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    References listed on IDEAS

    as
    1. 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.
    2. Enzo Busseti & Walaa M. Moursi & Stephen Boyd, 2019. "Solution refinement at regular points of conic problems," Computational Optimization and Applications, Springer, vol. 74(3), pages 627-643, December.
    3. 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.
    4. 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.
    Full references (including those not matched with items on IDEAS)

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