Research map / Optimization / Optimizers
FSNet: Feasibility-Seeking Neural Network for Constrained Optimization with Guarantees
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes FSNet, which embeds a differentiable feasibility-seeking step (unconstrained L-BFGS minimization of constraint violation) after a neural network prediction, trained end-to-end with an unsupervised objective-plus-proximity loss to give feasible solutions for constrained parametric optimization.
Problem
Neural networks that approximate solutions to parametric constrained optimization problems often violate equality and inequality constraints, and existing constraint-enforcement methods (penalty, projection, iterative correction) have poor solution quality, high cost, or no guarantees.
Approach
Append a feasibility-seeking step that runs unrolled gradient-based minimization of a squared constraint-violation function, warm-started at the NN prediction, and train the whole pipeline end-to-end with a loss combining objective value and the distance moved by the feasibility step; theory gives exponential feasibility convergence under PL and smoothness assumptions.
Key results
- On 500-variable convex problems, FSNet achieves 0.041-0.143% mean optimality gap with near-zero constraint violations and 188x batch speedup over the solver for QP.
- On smooth nonconvex QCQP, FSNet reaches a mean optimality gap of -19.4% (better than the solver) with violations around 1e-6, at 85-3000x batch speedups over traditional solvers.
- FSNet with truncated unrolled differentiation shows essentially unchanged constraint violation and optimality gap for tracked iterations K' between 10 and 50.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use FSNet instead of the traditional solver | Convex QP, n=500 · Convex QP, n=500 | runtime, batch: 112.962\std{0.378} -> 0.599\std{1.8e-3} | Helped |
| use FSNet instead of the traditional solver | Convex QCQP, n=500 · Convex QCQP, n=500 | runtime, batch: 5508.419\std{44.220} -> 37.291\std{0.237} | Helped |
| use FSNet instead of the traditional solver | Convex SOCP, n=500 · Convex SOCP, n=500 | runtime, batch: 523.045\std{6.284} -> 14.313\std{0.073} | Helped |
| use FSNet instead of the traditional solver | Nonconvex QCQP · Nonconvex QCQP | optimality gap: -0.668\std{0.650} | Helped |
| use FSNet instead of the traditional solver | Nonconvex SOCP · Nonconvex SOCP | optimality gap: -2.3\e{3}\std{0.7\e{3}} | Helped |
| track 10 feasibility-seeking iterations instead of none during backpropagation (ablation) | FSNet · Convex QP, n=100 | optimality gap (%): 14.143\std{0.024} -> 0.015\std{0.001} | Helped |
| track 20 feasibility-seeking iterations instead of none during backpropagation (ablation) | FSNet · Convex QP, n=100 | optimality gap (%): 14.143\std{0.024} -> 0.011\std{0.001} | Helped |
| increase tracked iterations from 10 to 50 (ablation) | FSNet · Convex QP, n=100 | optimality gap (%): 0.015\std{0.001} -> 0.015\std{0.002} | No clear effect |
| track 10 feasibility-seeking iterations instead of none during backpropagation (ablation) | FSNet · Convex QCQP, n=100 | optimality gap (%): 37.174\std{0.148} -> 0.032\std{0.002} | Helped |
| increase tracked iterations from 10 to 50 (ablation) | FSNet · Convex QCQP, n=100 | optimality gap (%): 0.032\std{0.002} -> 0.035\std{0.003} | No clear effect |
Surprising findings
- Penalty and DC3 baselines attain negative optimality gaps on convex problems, which the authors attribute to returning infeasible points with low objective values.
- On nonconvex QCQP and SOCP, FSNet finds lower-objective local solutions than IPOPT.
Limitations
- Convergence theory relies on strong assumptions (L-smoothness, PL condition, global minimizer of F) that are not verified for the experimental problems.
- QP sequential runtime is slower than OSQP, and FSNet has higher overhead than other NN methods.
- Scalability to extremely large-scale problems is not established.
Experimental setup
Datasets: synthetic parametric optimization instances (QP, QCQP, SOCP, nonconvex and nonsmooth nonconvex variants) ACOPF dataset from prior work
Benchmarks: synthetic convex QP/QCQP/SOCP (100 and 500 variables) synthetic nonconvex QP/QCQP/SOCP synthetic nonsmooth nonconvex QP/QCQP/SOCP ACOPF IEEE 30-bus and 118-bus
Metrics: equality violation inequality violation optimality gap batch runtime sequential runtime
Baselines: OSQP SCS IPOPT Penalty Adaptive Penalty DC3 Projection (qpth) Reduced Solver
Builds on: DC3 amortized optimization unrolled differentiation
Closest papers by meaning
- Efficient Bisection Projection to Ensure Neural-Network Solution Feasibility for Optimization over General Set (ICML 2025 · similarity 0.86)
- Are Graph Neural Networks Optimal Approximation Algorithms? (NeurIPS 2024 · similarity 0.85)
- Optimization Proxies using Limited Labeled Data and Training Time -- A Semi-Supervised Bayesian Neural Network Approach (ICML 2025 · similarity 0.85)
- Near-Optimal Solutions of Constrained Learning Problems (ICLR 2024 · similarity 0.85)
- Feasibility-Aware Decision-Focused Learning for Predicting Parameters in the Constraints (NeurIPS 2025 · similarity 0.85)
- Learning Valid Dual Bounds in Constraint Programming: Boosted Lagrangian Decomposition with Self-Supervised Learning (AAAI 2025 · similarity 0.84)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.