FSNet: Feasibility-Seeking Neural Network for Constrained Optimization with Guarantees
This addresses the need for real-time, feasible solutions in applications where traditional solvers are too slow, though it is incremental as it builds on existing machine learning-based approaches.
The paper tackles the problem of efficiently solving constrained optimization problems with strict constraint enforcement, proposing FSNet which integrates a feasibility-seeking step to ensure constraint satisfaction and achieves solution quality comparable to traditional solvers at significantly faster speeds, e.g., with experiments across various optimization types.
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.