学习用神经网络和序列二次规划细化求解混合整数非线性规划
Learning to Solve Mixed-Integer Nonlinear Programming with Neural Networks and Sequential Quadratic Programming Refinement
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中文总结 AI 辅助
提出一个结合神经网络预测与SQP细化层的学习优化框架，用于求解模型预测控制和轨迹优化中的参数化混合整数非线性规划，提高鲁棒性并保持计算预算。
中文摘要 AI 辅助
我们提出了一种学习优化框架，用于求解模型预测控制和轨迹优化中出现的参数化混合整数非线性规划。该方法将神经网络预测与序列二次规划（SQP）细化层相结合。首先，使用监督和自监督损失的组合来训练神经网络，以预测整数解以及兼容的连续热启动。为了考虑预测的不准确性，训练后的预测器生成多个候选整数解，每个解都配有一个连续初始化。然后固定整数解，一个可微的SQP层在规定的迭代次数内细化相关的连续变量。SQP层的参数，包括曲率正则化和步长，经过训练以在每次迭代后改善可行性和目标值。通过将整数预测与基于连续优化的细化分开，所提出的框架提高了对不完美神经预测的鲁棒性，同时保持可预测的计算预算。我们在平面推箱子示例的接触和轨迹优化上展示了所提出的框架。
英文摘要
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.
发表机构
- University of Pennsylvania（宾夕法尼亚大学）
机构由 AI 辅助整理，请以论文原文为准。
