mlsanityData to 7 Oct 2026

DC3: A learning method for optimization with hard constraints

arXiv 2104.12225 ↗First posted 25 Apr 2021cs.LG math.OC stat.MLcited by 181

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Abstract (arXiv)

Large optimization problems with hard constraints arise in many settings, yet classical solvers are often prohibitively slow, motivating the use of deep networks as cheap "approximate solvers." Unfortunately, naive deep learning approaches typically cannot enforce the hard constraints of such problems, leading to infeasible solutions. In this work, we present Deep Constraint Completion and Correction (DC3), an algorithm to address this challenge. Specifically, this method enforces feasibility via a differentiable procedure, which implicitly completes partial solutions to satisfy equality constraints and unrolls gradient-based corrections to satisfy inequality constraints. We demonstrate the effectiveness of DC3 in both synthetic optimization tasks and the real-world setting of AC optimal power flow, where hard constraints encode the physics of the electrical grid. In both cases, DC3 achieves near-optimal objective values while preserving feasibility.

Key facts. Cited by 181 papers in the map (data through 7 Oct 2026). Builds on 22 of its 33 references that are in the map. First posted on arXiv 25 Apr 2021.

Builds on

22 of 33 references.

References · 22

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10 more
  1. 2017OSQP: An Operator Splitting Solver for Quadratic Programscited by 156
  2. 2019Learning Optimal Solutions for Extremely Fast AC Optimal Power Flowcited by 76
  3. 2018Learning for Constrained Optimization: Identifying Optimal Active Constraint Setscited by 36
  4. 2019Learning Warm-Start Points for AC Optimal Power Flowcited by 32
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 11; 2022: 24; 2023: 31; 2024: 33; 2025: 36; 2026: 46.

181 papers.

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  1. 2021Characterizing possible failure modes in physics-informed neural networkscited by 632
  2. 2022Tutorial on amortized optimizationcited by 83
  3. 2023NIFTY: Neural Object Interaction Fields for Guided Human Motion Synthesiscited by 78
  4. 2022Self-Supervised Primal-Dual Learning for Constrained Optimizationcited by 60
  5. 2021Physics-Informed Neural Networks for AC Optimal Power Flowcited by 52
  6. 2023On the Constrained Time-Series Generation Problemcited by 52
  7. 2025Physics-Constrained Flow Matching: Sampling Generative Models with Hard Constraintscited by 46
  8. 2022Deep Equilibrium Approaches to Diffusion Modelscited by 42
  9. 2021Adversarial Robustness with Semi-Infinite Constrained Learningcited by 39
  10. 2023End-to-End Feasible Optimization Proxies for Large-Scale Economic Dispatchcited by 35
  11. 2022Learning differentiable solvers for systems with hard constraintscited by 34
  12. 2023RAYEN: Imposition of Hard Convex Constraints on Neural Networkscited by 30
38 more
  1. 2022Hard-Constrained Deep Learning for Climate Downscalingcited by 29
  2. 2024HardNet: Hard-Constrained Neural Networks with Universal Approximation Guaranteescited by 29
  3. 2021Constraint-based graph network simulatorcited by 27
  4. 2024Scaling physics-informed hard constraints with mixture-of-expertscited by 24
  5. 2021Physics-Informed Neural Networks for Minimising Worst-Case Violations in DC Optimal Power Flowcited by 23
  6. 2022SurCo: Learning Linear Surrogates For Combinatorial Nonlinear Optimization Problemscited by 21
  7. 2022Guiding continuous operator learning through Physics-based boundary constraintscited by 21
  8. 2024CGD: Constraint-Guided Diffusion Policies for UAV Trajectory Planningcited by 21
  9. 2025Training-Free Constrained Generation With Stable Diffusion Modelscited by 20
  10. 2022Competitive Physics Informed Networkscited by 19
  11. 2024DiffuSolve: Diffusion-based Solver for Non-convex Trajectory Optimizationcited by 19
  12. 2025FSNet: Feasibility-Seeking Neural Network for Constrained Optimization with Guaranteescited by 19
  13. 2022Evaluating Model-free Reinforcement Learning toward Safety-critical Taskscited by 18
  14. 2023Deep Equilibrium Diffusion Restoration with Parallel Samplingcited by 17
  15. 2025Pinet: Optimizing hard-constrained neural networks with orthogonal projection layerscited by 17
  16. 2024Learning Constrained Optimization with Deep Augmented Lagrangian Methodscited by 16
  17. 2023OpenForest: A data catalogue for machine learning in forest monitoringcited by 15
  18. 2025ENFORCE: Nonlinear Constrained Learning with Adaptive-depth Neural Projectioncited by 15
  19. 2025Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraintscited by 14
  20. 2022Learning Soft Constraints From Constrained Expert Demonstrationscited by 13
  21. 2022Multiscale Neural Operator: Learning Fast and Grid-independent PDE Solverscited by 12
  22. 2022Confidence-Aware Graph Neural Networks for Learning Reliability Assessment Commitmentscited by 12
  23. 2023A New Computationally Simple Approach for Implementing Neural Networks with Output Hard Constraintscited by 12
  24. 2024LeGo-Drive: Language-enhanced Goal-oriented Closed-Loop End-to-End Autonomous Drivingcited by 12
  25. 2023Compact Optimization Learning for AC Optimal Power Flowcited by 11
  26. 2023Dual Conic Proxies for AC Optimal Power Flowcited by 11
  27. 2024Dual Lagrangian Learning for Conic Optimizationcited by 11
  28. 2025PGLearn -- An Open-Source Learning Toolkit for Optimal Power Flowcited by 11
  29. 2021Neural Fixed-Point Acceleration for Convex Optimizationcited by 10
  30. 2023Generative Modelling of Stochastic Actions with Arbitrary Constraints in Reinforcement Learningcited by 10
  31. 2024Learning with Logical Constraints but without Shortcut Satisfactioncited by 10
  32. 2024A Comprehensive Survey on Inverse Constrained Reinforcement Learning: Definitions, Progress and Challengescited by 10
  33. 2024BPQP: A Differentiable Convex Optimization Framework for Efficient End-to-End Learningcited by 10
  34. 2025Enforcing Hard Linear Constraints in Deep Learning Models with Decision Rulescited by 10
  35. 2022Physics-Informed Learning of Aerosol Microphysicscited by 9
  36. 2023Energy-based Potential Games for Joint Motion Forecasting and Controlcited by 9
  37. 2025Adaptive Resource Allocation Optimization Using Large Language Models in Dynamic Wireless Environmentscited by 9
  38. 2024Learning to Optimize for Mixed-Integer Non-linear Programming with Feasibility Guaranteescited by 8

50 most cited of 181 All 181 (JSON)