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).

翻译：本文提出ODYN，一种新颖的全偏移原始-对偶非内点二次规划求解器，旨在高效处理具有挑战性的稠密与稀疏二次规划问题。ODYN将全偏移非线性互补问题函数与乘子近端法相结合，能够稳健处理病态及退化问题，且不要求约束条件线性独立。该方法展现出优异的热启动性能，既适用于通用优化问题，也特别适合机器人及人工智能应用场景，包括基于模型的控制、状态估计以及核学习方法。我们提供了开源实现，并在Maros-Mészáros测试集上对ODYN进行基准评估，结果表明该方法在中小规模至大规模问题上均达到当前最优的收敛性能。结果突显了ODYN卓越的热启动能力，这对机器人及人工智能领域常见的序列化与实时计算场景至关重要。通过将ODYN部署为基于序列二次规划的预测控制框架后端、深度学习隐式可微优化层以及接触动力学仿真优化器，进一步验证了其实际应用优势。