mlsanityData to 7 Oct 2026

Dual Lagrangian Learning for Conic Optimization

arXiv 2402.03086 ↗First posted 5 Feb 2024math.OC cs.LGcited by 11

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Abstract (arXiv)

This paper presents Dual Lagrangian Learning (DLL), a principled learning methodology for dual conic optimization proxies. DLL leverages conic duality and the representation power of ML models to provide high-duality, dual-feasible solutions, and therefore valid Lagrangian dual bounds, for linear and nonlinear conic optimization problems. The paper introduces a systematic dual completion procedure, differentiable conic projection layers, and a self-supervised learning framework based on Lagrangian duality. It also provides closed-form dual completion formulae for broad classes of conic problems, which eliminate the need for costly implicit layers. The effectiveness of DLL is demonstrated on linear and nonlinear conic optimization problems. The proposed methodology significantly outperforms a state-of-the-art learning-based method, and achieves 1000x speedups over commercial interior-point solvers with optimality gaps under 0.5% on average.

Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). Builds on 23 of its 42 references that are in the map. First posted on arXiv 5 Feb 2024.

Builds on

23 of 42 references.

References · 23

  1. 2021Convex optimizationcited by 2,479
  2. 2018Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizoncited by 612
  3. 2016Neural Combinatorial Optimization with Reinforcement Learningcited by 600
  4. 2017Learning Combinatorial Optimization Algorithms over Graphscited by 557
  5. 2019Differentiable Convex Optimization Layerscited by 458
  6. 2021DC3: A learning method for optimization with hard constraintscited by 181
  7. 2021End-to-End Constrained Optimization Learning: A Surveycited by 154
  8. 2019Predicting AC Optimal Power Flows: Combining Deep Learning and Lagrangian Dual Methodscited by 93
  9. 2019Differentiating Through a Cone Programcited by 72
  10. 2022Self-Supervised Primal-Dual Learning for Constrained Optimizationcited by 60
  11. 2018Fashionable Modelling with Fluxcited by 53
  12. 2019DeepOPF: A Deep Neural Network Approach for Security-Constrained DC Optimal Power Flowcited by 50
11 more
  1. 2018Don't Unroll Adjoint: Differentiating SSA-Form Programscited by 44
  2. 2023End-to-End Feasible Optimization Proxies for Large-Scale Economic Dispatchcited by 35
  3. 2023RAYEN: Imposition of Hard Convex Constraints on Neural Networkscited by 30
  4. 2023Exploring the Power of Graph Neural Networks in Solving Linear Optimization Problemscited by 24
  5. 2022Learning to Solve Optimization Problems with Hard Linear Constraintscited by 23
  6. 2023A New Computationally Simple Approach for Implementing Neural Networks with Output Hard Constraintscited by 12
  7. 2023Dual Conic Proxies for AC Optimal Power Flowcited by 11
  8. 2022Learning Regionally Decentralized AC Optimal Power Flows with ADMMcited by 7
  9. 2021Use of Machine Learning Models to Warmstart Column Generation for Unit Commitmentcited by 5
  10. 2020Solving natural conic formulations with Hypatia.jlcited by 4
  11. 2015Extended Formulations in Mixed-integer Convex Programmingcited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 7; 2026: 4.

11 papers.

  1. 2025FSNet: Feasibility-Seeking Neural Network for Constrained Optimization with Guaranteescited by 19
  2. 2025PGLearn -- An Open-Source Learning Toolkit for Optimal Power Flowcited by 11
  3. 2025Tightening optimality gap with confidence through conformal predictioncited by 2
  4. 2025Dual Conic Proxy for Semidefinite Relaxation of AC Optimal Power Flowcited by 1
  5. 2025ID-PaS+ : Identity-Aware Predict-and-Search for General Mixed-Integer Linear Programscited by 1
  6. 2026Learning to Optimize by Differentiable Programmingcited by 1
  7. 2026On the Expressive Power of GNNs to Solve Linear SDPscited by 1
  8. 2025Some Optimizers are More Equal: Understanding the Role of Optimizers in Group Fairnesscited by 0
  9. 2025Self-Certifying Primal-Dual Optimization Proxies for Large-Scale Batch Economic Dispatchcited by 0
  10. 2026Solving Max-Cut to Global Optimality via Feasibility-Preserving Graph Neural Networkscited by 0
  11. 2026Fusing Backdoors, Machine Learning, and Optimization for Large-Scale Parametric Mixed-Integer Programscited by 0