mlsanityData to 14 Oct 2026

Dual Conic Proxies for AC Optimal Power Flow

arXiv 2310.02969 ↗First posted 4 Oct 2023cs.LG math.OCcited by 11

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Abstract (arXiv)

In recent years, there has been significant interest in the development of machine learning-based optimization proxies for AC Optimal Power Flow (AC-OPF). Although significant progress has been achieved in predicting high-quality primal solutions, no existing learning-based approach can provide valid dual bounds for AC-OPF. This paper addresses this gap by training optimization proxies for a convex relaxation of AC-OPF. Namely, the paper considers a second-order cone (SOC) relaxation of AC-OPF, and proposes revisiona novel architecture that embeds a fast, differentiable (dual) feasibility recovery, thus providing valid dual bounds. The paper combines this new architecture with a self-supervised learning scheme, which alleviates the need for costly training data generation. Extensive numerical experiments on medium- and large-scale power grids demonstrate the efficiency and scalability of the proposed methodology.

Key facts. Cited by 11 papers in the map (data through 14 Oct 2026). Builds on 32 of its 47 references that are in the map. First posted on arXiv 4 Oct 2023.

Builds on

32 of 47 references.

References · 32

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  3. 2021DC3: A learning method for optimization with hard constraintscited by 184
  4. 2019Predicting AC Optimal Power Flows: Combining Deep Learning and Lagrangian Dual Methodscited by 94
  5. 2019Learning Optimal Solutions for Extremely Fast AC Optimal Power Flowcited by 77
  6. 2019The Power Grid Library for Benchmarking AC Optimal Power Flow Algorithmscited by 65
  7. 2022Self-Supervised Primal-Dual Learning for Constrained Optimizationcited by 61
  8. 2021Physics-Informed Neural Networks for AC Optimal Power Flowcited by 54
  9. 2019DeepOPF: A Deep Neural Network Approach for Security-Constrained DC Optimal Power Flowcited by 50
  10. 2020DeepOPF: A Feasibility-Optimized Deep Neural Network Approach for AC Optimal Power Flow Problemscited by 47
  11. 2023End-to-End Feasible Optimization Proxies for Large-Scale Economic Dispatchcited by 35
  12. 2017PowerModels.jl: An Open-Source Framework for Exploring Power Flow Formulationscited by 33
20 more
  1. 2019Learning for DC-OPF: Classifying active sets using neural netscited by 31
  2. 2021Learning Optimization Proxies for Large-Scale Security-Constrained Economic Dispatchcited by 29
  3. 2020Learning Optimal Power Flow: Worst-Case Guarantees for Neural Networkscited by 28
  4. 2021Physics-Informed Neural Networks for Minimising Worst-Case Violations in DC Optimal Power Flowcited by 23
  5. 2022Learning to Solve Optimization Problems with Hard Linear Constraintscited by 23
  6. 2021DeepOPF-V: Solving AC-OPF Problems Efficientlycited by 18
  7. 2014Convex Relaxation of Optimal Power Flow, Part I: Formulations and Equivalencecited by 17
  8. 2021Spatial Network Decomposition for Fast and Scalable AC-OPF Learningcited by 15
  9. 2022Unsupervised Optimal Power Flow Using Graph Neural Networkscited by 14
  10. 2023Compact Optimization Learning for AC Optimal Power Flowcited by 11
  11. 2014Convex Relaxation of Optimal Power Flow, Part II: Exactnesscited by 10
  12. 2015Strong SOCP Relaxations for the Optimal Power Flow Problemcited by 9
  13. 2018Efficient Database Generation for Data-driven Security Assessment of Power Systemscited by 9
  14. 2019Efficient Creation of Datasets for Data-Driven Power System Applicationscited by 9
  15. 2022Learning Regionally Decentralized AC Optimal Power Flows with ADMMcited by 7
  16. 2022Global Performance Guarantees for Neural Network Models of AC Power Flowcited by 4
  17. 2023GPU-Accelerated Verification of Machine Learning Models for Power Systemscited by 4
  18. 2014AC-Feasibility on Tree Networks is NP-Hardcited by 3
  19. 2019Proving Global Optimality of ACOPF Solutionscited by 3
  20. 2013Moment-Based Relaxation of the Optimal Power Flow Problemcited by 1

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Cited by year

Citing papers per year: 2024: 4; 2025: 7.

11 papers.

  1. 2024Learning Constrained Optimization with Deep Augmented Lagrangian Methodscited by 16
  2. 2024Dual Lagrangian Learning for Conic Optimizationcited by 11
  3. 2025PGLearn -- An Open-Source Learning Toolkit for Optimal Power Flowcited by 11
  4. 2025MSR-Align: Policy-Grounded Multimodal Alignment for Safety-Aware Reasoning in Vision-Language Modelscited by 7
  5. 2024Dual Interior Point Optimization Learningcited by 4
  6. 2025Efficient End-to-End Learning for Decision-Making: A Meta-Optimization Approachcited by 3
  7. 2025Flow-Aware GNN for Transmission Network Reconfiguration via Substation Breaker Optimizationcited by 3
  8. 2024Compact Optimality Verification for Optimization Proxiescited by 2
  9. 2025Tightening optimality gap with confidence through conformal predictioncited by 2
  10. 2025Sobolev Training of End-to-End Optimization Proxiescited by 2
  11. 2025Dual Conic Proxy for Semidefinite Relaxation of AC Optimal Power Flowcited by 1