# HoP: Homeomorphic Polar Learning for Hard Constrained Optimization

arXiv: https://arxiv.org/abs/2502.00304 · HTML: https://mlsanity.com/paper/2502.00304/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 30 references that are in the map.
- First posted on arXiv 1 Feb 2025.

## Builds on (most cited first, 20 of 20)

- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (2021)
- [Learning to Optimize: Training Deep Neural Networks for Wireless Resource Management](https://mlsanity.com/paper/1705.09412/) (2017)
- [Learning Optimal Solutions for Extremely Fast AC Optimal Power Flow](https://mlsanity.com/paper/1910.01213/) (2019)
- [Self-Supervised Primal-Dual Learning for Constrained Optimization](https://mlsanity.com/paper/2208.09046/) (2022)
- [Learning for Constrained Optimization: Identifying Optimal Active Constraint Sets](https://mlsanity.com/paper/1802.09639/) (2018)
- [Learning differentiable solvers for systems with hard constraints](https://mlsanity.com/paper/2207.08675/) (2022)
- [HardNet: Hard-Constrained Neural Networks with Universal Approximation Guarantees](https://mlsanity.com/paper/2410.10807/) (2024)
- [Machine Learning for AC Optimal Power Flow](https://mlsanity.com/paper/1910.08842/) (2019)
- [Learning to Solve Optimization Problems with Hard Linear Constraints](https://mlsanity.com/paper/2208.10611/) (2022)
- [A Survey of Recent Advances in Optimization Methods for Wireless Communications](https://mlsanity.com/paper/2401.12025/) (2024)
- [DeepOPF-V: Solving AC-OPF Problems Efficiently](https://mlsanity.com/paper/2103.11793/) (2021)
- [Resilient Constrained Learning](https://mlsanity.com/paper/2306.02426/) (2023)
- [Constrained Reinforcement Learning with Smoothed Log Barrier Function](https://mlsanity.com/paper/2403.14508/) (2024)
- [Neural Fields with Hard Constraints of Arbitrary Differential Order](https://mlsanity.com/paper/2306.08943/) (2023)
- [Towards An Efficient Approach for the Nonconvex ℓp Ball Projection: Algorithm and Analysis](https://mlsanity.com/paper/2101.01350/) (2021)
- [Self-supervised Equality Embedded Deep Lagrange Dual for Approximate Constrained Optimization](https://mlsanity.com/paper/2306.06674/) (2023)

## Built on by (most cited first, 1 of 1)

- [Soft-Radial Projection for Constrained End-to-End Learning](https://mlsanity.com/paper/2602.03461/) (2026)

## Abstract (arXiv)

Constrained optimization demands highly efficient solvers which promotes the development of learn-to-optimize (L2O) approaches. As a data-driven method, L2O leverages neural networks to efficiently produce approximate solutions. However, a significant challenge remains in ensuring both optimality and feasibility of neural networks' output. To tackle this issue, we introduce Homeomorphic Polar Learning (HoP) to solve the star-convex hard-constrained optimization by embedding homeomorphic mapping in neural networks. The bijective structure enables end-to-end training without extra penalty or correction. For performance evaluation, we evaluate HoP's performance across a variety of synthetic optimization tasks and real-world applications in wireless communications. In all cases, HoP achieves solutions closer to the optimum than existing L2O methods while strictly maintaining feasibility.