FSNet: Feasibility-Seeking Neural Network for Constrained Optimization with Guarantees
Hoang T. Nguyen, Priya L. Donti
TL;DR
FSNet introduces a Feasibility-Seeking Neural Network that embeds a differentiable feasibility-correction step into both training and inference to solve constrained optimization problems efficiently with guarantees on feasibility and convergence. The core idea is to start from a neural predictor $\hat{y}_{\theta}(x)$ and refine it via an unconstrained feasibility objective $\phi(s;x)=\|h(s;x)\|_2^2+\|g^+(s;x)\|_2^2$, producing $\hat{y}_{\theta}(x)$ while backpropagating through the unrolled iterations to train end-to-end. Theoretical results show exponential convergence of the feasibility-seeking step under standard smoothness/PL assumptions, convergence of SGD training to a stationary point with a bias that decays with unrolling depth, and conditions under which FSNet recovers the true constrained minimizer via a penalty parameter ramp. Empirically, FSNet achieves near-zero constraint violations and competitive or superior objective values across convex, nonconvex, and ACOPF problems, delivering order-of-magnitude speedups over traditional solvers, especially for large-scale batch scenarios. This combination of feasibility guarantees and speed makes FSNet a practical alternative for real-time, safety-critical optimization tasks across engineering domains.
Abstract
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.