mlsanityData to 14 Oct 2026

On the Differentiability of the Solution to Convex Optimization Problems

arXiv 1804.05098 ↗First posted 13 Apr 2018math.OCcited by 23

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Abstract (arXiv)

In this paper, we provide conditions under which one can take derivatives of the solution to convex optimization problems with respect to problem data. These conditions are (roughly) that Slater's condition holds, the functions involved are twice differentiable, and that a certain Jacobian matrix is non-singular. The derivation involves applying the implicit function theorem to the necessary and sufficient KKT system for optimality.

Key facts. Cited by 23 papers in the map (data through 14 Oct 2026). First posted on arXiv 13 Apr 2018.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 3; 2022: 8; 2023: 3; 2024: 4; 2025: 2; 2026: 3.

23 papers.

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  1. 2022Tutorial on amortized optimizationcited by 83
  2. 2021Learnable Graph Matching: Incorporating Graph Partitioning with Deep Feature Learning for Multiple Object Trackingcited by 47
  3. 2022Learning differentiable solvers for systems with hard constraintscited by 34
  4. 2022Alternating Differentiation for Optimization Layerscited by 22
  5. 2022Partially Does It: Towards Scene-Level FG-SBIR with Partial Inputcited by 20
  6. 2024Mechanistic Neural Networks for Scientific Machine Learningcited by 16
  7. 2021The Perils of Learning Before Optimizingcited by 15
  8. 2022Learning of Global Objective for Network Flow in Multi-Object Trackingcited by 11
  9. 2025Conformal Risk Training: End-to-End Optimization of Conformal Risk Controlcited by 11
  10. 2022Hierarchical Compositional Representations for Few-shot Action Recognitioncited by 10
  11. 2022Differentiable Mathematical Programming for Object-Centric Representation Learningcited by 6
  12. 2023The Pursuit of Human Labeling: A New Perspective on Unsupervised Learningcited by 6
11 more
  1. 2021End-to-End Demand Response Model Identification and Baseline Estimation with Deep Learningcited by 3
  2. 2025The Bias-Variance Tradeoff in Data-Driven Optimization: A Local Misspecification Perspectivecited by 3
  3. 2023Learnable Graph Matching: A Practical Paradigm for Data Associationcited by 2
  4. 2023Efficient Sensitivity Analysis for Parametric Robust Markov Chainscited by 2
  5. 2024Differentiable Convex Optimization Layers in Neural Architectures: Foundations and Perspectivescited by 2
  6. 2022Second-Order Sensitivity Analysis for Bilevel Optimizationcited by 1
  7. 2024Learning and Optimization for Price-based Demand Response of Electric Vehicle Chargingcited by 1
  8. 2026Learning to Optimize by Differentiable Programmingcited by 1
  9. 2024AMOSL: Adaptive Modality-wise Structure Learning in Multi-view Graph Neural Networks For Enhanced Unified Representationcited by 0
  10. 2026Efficient and provably convergent end-to-end training of deep neural networks with linear constraintscited by 0
  11. 2026dOPT: Differentiating Conic Optimization via Geometric Reductioncited by 0