Flexible Differentiable Optimization via Model Transformations

Mathieu Besançon (), Joaquim Dias Garcia (), Benoît Legat () and Akshay Sharma ()
Additional contact information
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

INFORMS Journal on Computing, 2024, vol. 36, issue 2, 456-478

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.

Keywords: differentiable optimization; implicit differentiation; automatic differentiation; convex optimization; conic optimization (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://dx.doi.org/10.1287/ijoc.2022.0283 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:orijoc:v:36:y:2024:i:2:p:456-478

Access Statistics for this article

More articles in INFORMS Journal on Computing from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().