ODYN：一种用于机器人和人工智能中二次规划的全位移非内点法
ODYN: An All-Shifted Non-Interior-Point Method for Quadratic Programming in Robotics and AI
AI总结：
ODYN是一种全新的全位移对偶非内点二次规划求解器，能高效处理密集和稀疏二次规划问题，通过结合全位移非线性互补问题函数与近端乘子法，解决病态和退化问题，具备强大的热启动性能，适用于通用优化及机器人和人工智能应用。
摘要：
我们介绍了ODYN，一种新的全位移对偶非内点二次规划（QP）求解器，旨在高效处理具有挑战性的密集和稀疏QP。ODYN结合了全位移非线性互补问题（NCP）函数与近端乘子法，以稳健地解决病态和退化问题，而无需要求约束的线性独立性。它表现出强大的热启动性能，并适用于通用优化以及机器人和人工智能应用，包括基于模型的控制、估计和基于核的学习方法。我们提供了一个开源实现，并在Maros-Mészáros测试集上对ODYN进行了基准测试，展示了在小到大规模问题中先进的收敛性能。结果突显了ODYN的优越热启动能力，这对于序列和实时设置至关重要，这些在机器人和人工智能中很常见。这些优势进一步通过将ODYN作为基于SQP的预测控制框架（OdynSQP）的后端、作为深度学习的隐式可微优化层（ODYNLayer）以及接触动力学模拟的优化器来演示。
英文摘要：
We introduce ODYN, a novel all-shifted primal-dual non-interior-point quadratic programming (QP) solver designed to efficiently handle challenging dense and sparse QPs. ODYN combines all-shifted nonlinear complementarity problem (NCP) functions with proximal method of multipliers to robustly address ill-conditioned and degenerate problems, without requiring linear independence of the constraints. It exhibits strong warm-start performance and is well suited to both general-purpose optimization, and robotics and AI applications, including model-based control, estimation, and kernel-based learning methods. We provide an open-source implementation and benchmark ODYN on the Maros-Mészáros test set, demonstrating state-of-the-art convergence performance in small-to-high-scale problems. The results highlight ODYN's superior warm-starting capabilities, which are critical in sequential and real-time settings common in robotics and AI. These advantages are further demonstrated by deploying ODYN as the backend of an SQP-based predictive control framework (OdynSQP), as the implicitly differentiable optimization layer for deep learning (ODYNLayer), and the optimizer of a contact-dynamics simulation (ODYNSim).
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