mlsanityData to 7 Oct 2026

Flexible Differentiable Optimization via Model Transformations

arXiv 2206.06135 ↗First posted 10 Jun 2022cs.LG cs.MS math.OCcited by 16

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Abstract (arXiv)

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 ability to differentiate through model transformation, 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.

Key facts. Cited by 16 papers in the map (data through 7 Oct 2026). Builds on 19 of its 63 references that are in the map. First posted on arXiv 10 Jun 2022.

Builds on

19 of 63 references.

References · 19

  1. 2017OptNet: Differentiable Optimization as a Layer in Neural Networkscited by 588
  2. 2019Meta-Learning with Differentiable Convex Optimizationcited by 461
  3. 2019Differentiable Convex Optimization Layerscited by 458
  4. 2015Gradient-based Hyperparameter Optimization through Reversible Learningcited by 357
  5. 2021Efficient and Modular Implicit Differentiationcited by 199
  6. 2020Fast Differentiable Sorting and Rankingcited by 196
  7. 2017OSQP: An Operator Splitting Solver for Quadratic Programscited by 156
  8. 2021End-to-End Constrained Optimization Learning: A Surveycited by 154
  9. 2019A Differentiable Programming System to Bridge Machine Learning and Scientific Computingcited by 81
  10. 2019Differentiating Through a Cone Programcited by 72
  11. 2015JuMP: A Modeling Language for Mathematical Optimizationcited by 49
  12. 2021CombOptNet: Fit the Right NP-Hard Problem by Learning Integer Programming Constraintscited by 49
7 more
  1. 2020A mathematical model for automatic differentiation in machine learningcited by 44
  2. 2018Solution Refinement at Regular Points of Conic Problemscited by 21
  3. 2020MathOptInterface: a data structure for mathematical optimization problemscited by 9
  4. 2018Provably Correct Automatic Subdifferentiation for Qualified Programscited by 8
  5. 2020Differentiating through Log-Log Convex Programscited by 7
  6. 2020Solving natural conic formulations with Hypatia.jlcited by 4
  7. 2021AbstractDifferentiation.jl: Backend-Agnostic Differentiable Programming in Juliacited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 1; 2024: 1; 2025: 4; 2026: 9.

16 papers.

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  1. 2022Learning with Combinatorial Optimization Layers: a Probabilistic Approachcited by 28
  2. 2024Differentiation Through Black-Box Quadratic Programming Solverscited by 10
  3. 2025A General and Streamlined Differentiable Optimization Frameworkcited by 3
  4. 2025A Fully First-Order Layer for Differentiable Optimizationcited by 3
  5. 2025Sobolev Training of End-to-End Optimization Proxiescited by 2
  6. 2025Differentiable Optimization for Deep Learning-Enhanced DC Approximation of AC Optimal Power Flowcited by 1
  7. 2026Batched First-Order Methods for Parallel LP Solving in MIPcited by 1
  8. 2026SOC-ICNN: From Polyhedral to Conic Geometry for Learning Convex Surrogate Functionscited by 1
  9. 2026Relaxation-Informed Training of Neural Network Surrogate Modelscited by 1
  10. 2023Price-Aware Deep Learning for Electricity Marketscited by 0
  11. 2026partialCBDs: Differentiable Causal Block Diagramscited by 0
  12. 2026DisjunctiveNet: Neural Symbolic Learning via Differentiable Convexified Optimization Layerscited by 0
4 more
  1. 2026Elastic ODYN: Differentiable Optimization for Infeasible Control and Learning in Roboticscited by 0
  2. 2026TorchDCM: A Unified PyTorch-Native Package for Discrete Choice Modelingcited by 0
  3. 2026Differentiable Electricity-Market Clearing for Gradient-Based Planningcited by 0
  4. 2026dOPT: Differentiating Conic Optimization via Geometric Reductioncited by 0