# FSNet: Feasibility-Seeking Neural Network for Constrained Optimization with Guarantees

arXiv: https://arxiv.org/abs/2506.00362 · HTML: https://mlsanity.com/paper/2506.00362/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 51 references that are in the map.
- First posted on arXiv 31 May 2025.

## Builds on (most cited first, 30 of 40)

- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Condition](https://mlsanity.com/paper/1608.04636/) (2016)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Efficient and Modular Implicit Differentiation](https://mlsanity.com/paper/2105.15183/) (2021)
- [Truncated Back-propagation for Bilevel Optimization](https://mlsanity.com/paper/1810.10667/) (2018)
- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (2021)
- [OSQP: An Operator Splitting Solver for Quadratic Programs](https://mlsanity.com/paper/1711.08013/) (2017)
- [Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities](https://mlsanity.com/paper/2307.13565/) (2023)
- [Tutorial on amortized optimization](https://mlsanity.com/paper/2202.00665/) (2022)
- [Deep Declarative Networks: A New Hope](https://mlsanity.com/paper/1909.04866/) (2019)
- [Learning Optimal Solutions for Extremely Fast AC Optimal Power Flow](https://mlsanity.com/paper/1910.01213/) (2019)
- [Lagrangian Duality for Constrained Deep Learning](https://mlsanity.com/paper/2001.09394/) (2020)
- [Differentiating Through a Cone Program](https://mlsanity.com/paper/1904.09043/) (2019)
- [Self-Supervised Primal-Dual Learning for Constrained Optimization](https://mlsanity.com/paper/2208.09046/) (2022)
- [Enforcing robust control guarantees within neural network policies](https://mlsanity.com/paper/2011.08105/) (2020)
- [Learning for Constrained Optimization: Identifying Optimal Active Constraint Sets](https://mlsanity.com/paper/1802.09639/) (2018)
- [Physics-constrained Deep Learning of Multi-zone Building Thermal Dynamics](https://mlsanity.com/paper/2011.05987/) (2020)
- [Learning to Warm-Start Fixed-Point Optimization Algorithms](https://mlsanity.com/paper/2309.07835/) (2023)
- [RAYEN: Imposition of Hard Convex Constraints on Neural Networks](https://mlsanity.com/paper/2307.08336/) (2023)
- [Learning Optimization Proxies for Large-Scale Security-Constrained Economic Dispatch](https://mlsanity.com/paper/2112.13469/) (2021)
- [Operator splitting for a homogeneous embedding of the linear complementarity problem](https://mlsanity.com/paper/2004.02177/) (2020)
- [ENFORCE: Nonlinear Constrained Learning with Adaptive-depth Neural Projection](https://mlsanity.com/paper/2502.06774/) (2025)
- [The Curse of Unrolling: Rate of Differentiating Through Optimization](https://mlsanity.com/paper/2209.13271/) (2022)
- [Optimization Learning](https://mlsanity.com/paper/2501.03443/) (2025)
- [Backpropagation of Unrolled Solvers with Folded Optimization](https://mlsanity.com/paper/2301.12047/) (2023)
- [A New Computationally Simple Approach for Implementing Neural Networks with Output Hard Constraints](https://mlsanity.com/paper/2307.10459/) (2023)
- [Compact Optimization Learning for AC Optimal Power Flow](https://mlsanity.com/paper/2301.08840/) (2023)
- [Dual Lagrangian Learning for Conic Optimization](https://mlsanity.com/paper/2402.03086/) (2024)

## Built on by (most cited first, 21 of 21)

- [Towards Generalization of Graph Neural Networks for AC Optimal Power Flow](https://mlsanity.com/paper/2510.06860/) (2025)
- [GENCO - A Unified Neural Solver Embedded in a Development Framework for Steady-State Grid Analysis](https://mlsanity.com/paper/2608.09921/) (2026)
- [Safe Reinforcement Learning using Action Projection: Safeguard the Policy or the Environment?](https://mlsanity.com/paper/2509.12833/) (2025)
- [Improving Feasibility via Fast Autoencoder-Based Projections](https://mlsanity.com/paper/2604.03489/) (2026)
- [SnareNet: Flexible Repair Layers for Neural Networks with Hard Constraints](https://mlsanity.com/paper/2602.09317/) (2026)
- [HardNet++: Nonlinear Constraint Enforcement in Neural Networks](https://mlsanity.com/paper/2604.19669/) (2026)
- [T-SKM-Net: Trainable Neural Network Framework for Linear Constraint Satisfaction via Sampling Kaczmarz-Motzkin Method](https://mlsanity.com/paper/2512.10461/) (2025)
- [Cheap Thrills: Effective Amortized Optimization Using Inexpensive Labels](https://mlsanity.com/paper/2603.05495/) (2026)
- [LEAF: A Learning-Enabled ADMM Framework for Accelerated Convex Optimization](https://mlsanity.com/paper/2606.08993/) (2026)
- [HUANet: Hard-Constrained Unrolled ADMM for Constrained Convex Optimization](https://mlsanity.com/paper/2604.13179/) (2026)
- [A Multi-Stage Warm-Start Deep Learning Framework for Unit Commitment](https://mlsanity.com/paper/2604.21891/) (2026)
- [CAffNet: Hard Constraint-Affine Neural Networks](https://mlsanity.com/paper/2605.24437/) (2026)
- [DisjunctiveNet: Neural Symbolic Learning via Differentiable Convexified Optimization Layers](https://mlsanity.com/paper/2605.30456/) (2026)
- [Rethinking Neural Width for Alternating Current Optimal Power Flow Proxies](https://mlsanity.com/paper/2606.03125/) (2026)
- [Multi-ResNets for Subspace Preconditioning in Constrained Optimization](https://mlsanity.com/paper/2606.06300/) (2026)
- [FunL2O: LLM-Guided Feature Function Design for Learning to Optimize](https://mlsanity.com/paper/2607.27389/) (2026)
- [Scalable Self-Supervised Learning for Multiphase AC-OPF in Distribution Systems with Topology Reconfiguration](https://mlsanity.com/paper/2608.25095/) (2026)
- [GridSFM: A Foundation Model for Solving AC Optimal Power Flow](https://mlsanity.com/paper/2609.30173/) (2026)
- [SLP-ProbHard: Probabilistic Hard-Constrained Learning via Structural Latent Parameterization](https://mlsanity.com/paper/2609.33515/) (2026)
- [Only Project Once: Projection-Adaptive Loss for Exact Constraint Satisfaction](https://mlsanity.com/paper/2610.04572/) (2026)
- [Physics-Informed but Not Physics-Consistent: Error Geometry and Subspace Projection for Neural AC Power Flow](https://mlsanity.com/paper/2610.05959/) (2026)

## Abstract (arXiv)

Efficiently solving constrained optimization problems is crucial for numerous real-world applications, yet traditional solvers are often computationally prohibitive for real-time use. Machine learning-based approaches have emerged as a promising alternative to provide approximate solutions at faster speeds, but they struggle to strictly enforce constraints, leading to infeasible solutions in practice. To address this, we propose the Feasibility-Seeking Neural Network (FSNet), which integrates a feasibility-seeking step directly into its solution procedure to ensure constraint satisfaction. This feasibility-seeking step solves an unconstrained optimization problem that minimizes constraint violations in a differentiable manner, enabling end-to-end training and providing guarantees on feasibility and convergence. Our experiments across a range of different optimization problems, including both smooth/nonsmooth and convex/nonconvex problems, demonstrate that FSNet can provide feasible solutions with solution quality comparable to (or in some cases better than) traditional solvers, at significantly faster speeds.