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

TL;DR

FSNet is a neural network designed for constrained optimization that guarantees feasibility by integrating a differentiable feasibility step, achieving comparable solution quality to traditional methods with much faster computation.

Contribution

Introduces FSNet, a neural network with an embedded feasibility-seeking step that ensures constraint satisfaction and guarantees convergence in constrained optimization.

Findings

Provides feasible solutions with quality comparable to traditional solvers

Achieves significantly faster solution times

Works across various types of optimization problems

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.