# Dual Interior Point Optimization Learning

arXiv: https://arxiv.org/abs/2402.02596 · HTML: https://mlsanity.com/paper/2402.02596/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 16 references that are in the map.
- First posted on arXiv 4 Feb 2024.

## Builds on (most cited first, 10 of 10)

- [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)
- [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)
- [End-to-End Feasible Optimization Proxies for Large-Scale Economic Dispatch](https://mlsanity.com/paper/2304.11726/) (2023)
- [Practical Large-Scale Linear Programming using Primal-Dual Hybrid Gradient](https://mlsanity.com/paper/2106.04756/) (2021)
- [Exploring the Power of Graph Neural Networks in Solving Linear Optimization Problems](https://mlsanity.com/paper/2310.10603/) (2023)
- [Dual Conic Proxies for AC Optimal Power Flow](https://mlsanity.com/paper/2310.02969/) (2023)
- [An ADMM-Based Interior-Point Method for Large-Scale Linear Programming](https://mlsanity.com/paper/1805.12344/) (2018)

## Built on by (most cited first, 4 of 4)

- [Towards graph neural networks for provably solving convex optimization problems](https://mlsanity.com/paper/2502.02446/) (2025)
- [Tightening optimality gap with confidence through conformal prediction](https://mlsanity.com/paper/2503.04071/) (2025)
- [Self-Certifying Primal-Dual Optimization Proxies for Large-Scale Batch Economic Dispatch](https://mlsanity.com/paper/2510.15850/) (2025)
- [WARP: A Benchmark for Primal-Dual Warm-Starting of Interior-Point Solvers](https://mlsanity.com/paper/2605.05728/) (2026)

## Abstract (arXiv)

In many practical applications of constrained optimization, scale and solving time limits make traditional optimization solvers prohibitively slow. Thus, the research question of how to design optimization proxies -- machine learning models that produce high-quality solutions -- has recently received significant attention. Orthogonal to this research thread which focuses on learning primal solutions, this paper studies how to learn dual feasible solutions that complement primal approaches and provide quality guarantees. The paper makes two distinct contributions. First, to train dual linear optimization proxies, the paper proposes a smoothed self-supervised loss function that augments the objective function with a dual penalty term. Second, the paper proposes a novel dual completion strategy that guarantees dual feasibility by solving a convex optimization problem. Moreover, the paper derives closed-form solutions to this completion optimization for several classes of dual penalties, eliminating the need for computationally-heavy implicit layers. Numerical results are presented on large linear optimization problems and demonstrate the effectiveness of the proposed approach. The proposed dual completion outperforms methods for learning optimization proxies which do not exploit the structure of the dual problem. Compared to commercial optimization solvers, the learned dual proxies achieve optimality gaps below 1% and several orders of magnitude speedups.