# Dual Conic Proxies for AC Optimal Power Flow

arXiv: https://arxiv.org/abs/2310.02969 · HTML: https://mlsanity.com/paper/2310.02969/

## 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 (most cited first, 30 of 32)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (2021)
- [Predicting AC Optimal Power Flows: Combining Deep Learning and Lagrangian Dual Methods](https://mlsanity.com/paper/1909.10461/) (2019)
- [Learning Optimal Solutions for Extremely Fast AC Optimal Power Flow](https://mlsanity.com/paper/1910.01213/) (2019)
- [The Power Grid Library for Benchmarking AC Optimal Power Flow Algorithms](https://mlsanity.com/paper/1908.02788/) (2019)
- [Self-Supervised Primal-Dual Learning for Constrained Optimization](https://mlsanity.com/paper/2208.09046/) (2022)
- [Physics-Informed Neural Networks for AC Optimal Power Flow](https://mlsanity.com/paper/2110.02672/) (2021)
- [DeepOPF: A Deep Neural Network Approach for Security-Constrained DC Optimal Power Flow](https://mlsanity.com/paper/1910.14448/) (2019)
- [DeepOPF: A Feasibility-Optimized Deep Neural Network Approach for AC Optimal Power Flow Problems](https://mlsanity.com/paper/2007.01002/) (2020)
- [End-to-End Feasible Optimization Proxies for Large-Scale Economic Dispatch](https://mlsanity.com/paper/2304.11726/) (2023)
- [PowerModels.jl: An Open-Source Framework for Exploring Power Flow Formulations](https://mlsanity.com/paper/1711.01728/) (2017)
- [Learning for DC-OPF: Classifying active sets using neural nets](https://mlsanity.com/paper/1902.05607/) (2019)
- [Learning Optimization Proxies for Large-Scale Security-Constrained Economic Dispatch](https://mlsanity.com/paper/2112.13469/) (2021)
- [Learning Optimal Power Flow: Worst-Case Guarantees for Neural Networks](https://mlsanity.com/paper/2006.11029/) (2020)
- [Physics-Informed Neural Networks for Minimising Worst-Case Violations in DC Optimal Power Flow](https://mlsanity.com/paper/2107.00465/) (2021)
- [Learning to Solve Optimization Problems with Hard Linear Constraints](https://mlsanity.com/paper/2208.10611/) (2022)
- [DeepOPF-V: Solving AC-OPF Problems Efficiently](https://mlsanity.com/paper/2103.11793/) (2021)
- [Convex Relaxation of Optimal Power Flow, Part I: Formulations and Equivalence](https://mlsanity.com/paper/1405.0766/) (2014)
- [Spatial Network Decomposition for Fast and Scalable AC-OPF Learning](https://mlsanity.com/paper/2101.06768/) (2021)
- [Unsupervised Optimal Power Flow Using Graph Neural Networks](https://mlsanity.com/paper/2210.09277/) (2022)
- [Compact Optimization Learning for AC Optimal Power Flow](https://mlsanity.com/paper/2301.08840/) (2023)
- [Convex Relaxation of Optimal Power Flow, Part II: Exactness](https://mlsanity.com/paper/1405.0814/) (2014)
- [Strong SOCP Relaxations for the Optimal Power Flow Problem](https://mlsanity.com/paper/1504.06770/) (2015)
- [Efficient Database Generation for Data-driven Security Assessment of Power Systems](https://mlsanity.com/paper/1806.01074/) (2018)
- [Efficient Creation of Datasets for Data-Driven Power System Applications](https://mlsanity.com/paper/1910.01794/) (2019)
- [Learning Regionally Decentralized AC Optimal Power Flows with ADMM](https://mlsanity.com/paper/2205.03787/) (2022)
- [Global Performance Guarantees for Neural Network Models of AC Power Flow](https://mlsanity.com/paper/2211.07125/) (2022)
- [GPU-Accelerated Verification of Machine Learning Models for Power Systems](https://mlsanity.com/paper/2306.10617/) (2023)
- [AC-Feasibility on Tree Networks is NP-Hard](https://mlsanity.com/paper/1410.8253/) (2014)

## Built on by (most cited first, 11 of 11)

- [Learning Constrained Optimization with Deep Augmented Lagrangian Methods](https://mlsanity.com/paper/2403.03454/) (2024)
- [Dual Lagrangian Learning for Conic Optimization](https://mlsanity.com/paper/2402.03086/) (2024)
- [PGLearn -- An Open-Source Learning Toolkit for Optimal Power Flow](https://mlsanity.com/paper/2505.22825/) (2025)
- [MSR-Align: Policy-Grounded Multimodal Alignment for Safety-Aware Reasoning in Vision-Language Models](https://mlsanity.com/paper/2506.19257/) (2025)
- [Dual Interior Point Optimization Learning](https://mlsanity.com/paper/2402.02596/) (2024)
- [Efficient End-to-End Learning for Decision-Making: A Meta-Optimization Approach](https://mlsanity.com/paper/2505.11360/) (2025)
- [Flow-Aware GNN for Transmission Network Reconfiguration via Substation Breaker Optimization](https://mlsanity.com/paper/2508.01951/) (2025)
- [Compact Optimality Verification for Optimization Proxies](https://mlsanity.com/paper/2405.21023/) (2024)
- [Tightening optimality gap with confidence through conformal prediction](https://mlsanity.com/paper/2503.04071/) (2025)
- [Sobolev Training of End-to-End Optimization Proxies](https://mlsanity.com/paper/2505.11342/) (2025)
- [Dual Conic Proxy for Semidefinite Relaxation of AC Optimal Power Flow](https://mlsanity.com/paper/2502.06978/) (2025)

## 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.