Learning to Solve Mixed-Integer Nonlinear Programming with Neural Networks and Sequential Quadratic Programming Refinement
Abstract
We propose a learning-to-optimize framework for solving parametric mixed-integer nonlinear programs arising in model predictive control and trajectory optimization. The proposed method combines neural network prediction with a sequential quadratic programming (SQP) refinement layer. First, neural networks are trained using a combination of supervised and self-supervised losses to predict integer solutions together with compatible continuous warm starts. To account for prediction inaccuracies, the trained predictor generates multiple candidate integer solutions, each paired with a continuous initialization. The integer solutions are then fixed, and a differentiable SQP layer refines the associated continuous variables over a prescribed number of iterations. The SQP-layer parameters, including the curvature regularization and step size, are trained to improve both feasibility and objective value after every iteration. By separating integer prediction from continuous optimization-based refinement, the proposed framework improves robustness to imperfect neural predictions while maintaining a predictable computational budget. We demonstrate the proposed framework on contact and trajectory optimization for a planar box-pushing example.
Related
- Adaptive Variance-Reduced Stochastic Sequential (Quadratic Constrained) Quadratic Programming
- Nonlinear Density-Driven Optimal Control (D2OC) for Multi-Agent Spatial Coverage via Sequential Convex Programming
- A quadratic refinement of Jackson's \CE\ condition for Hamilton cycles in digraphs
- cuPDQPx: A GPU-Accelerated Restarted Halpern PDHG for Large-Scale Convex Quadratic Programming
- Recent Developments in HPR Methods for Large-Scale Convex Composite Quadratic Programming
BibTeX
@misc{le2026learning,
title = {{Learning to Solve Mixed-Integer Nonlinear Programming with Neural Networks and Sequential Quadratic Programming Refinement}},
author = {Viet-Anh Le and Rahul Mangharam},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05746},
eprint = {2610.05746},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05746},
}
RIS
TY - UNPB
TI - Learning to Solve Mixed-Integer Nonlinear Programming with Neural Networks and Sequential Quadratic Programming Refinement
AU - Viet-Anh Le
AU - Rahul Mangharam
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.05746
UR - https://arxiv.org/abs/2610.05746
AB - We propose a learning-to-optimize framework for solving parametric mixed-integer nonlinear programs arising in model predictive control and trajectory optimization. The proposed method combines neural network prediction with a sequential quadratic programming (SQP) refinement layer. First, neural networks are trained using a combination of supervised and self-supervised losses to predict integer solutions together with compatible continuous warm starts. To account for prediction inaccuracies, the trained predictor generates multiple candidate integer solutions, each paired with a continuous initialization. The integer solutions are then fixed, and a differentiable SQP layer refines the associated continuous variables over a prescribed number of iterations. The SQP-layer parameters, including the curvature regularization and step size, are trained to improve both feasibility and objective value after every iteration. By separating integer prediction from continuous optimization-based refinement, the proposed framework improves robustness to imperfect neural predictions while maintaining a predictable computational budget. We demonstrate the proposed framework on contact and trajectory optimization for a planar box-pushing example.
ER -