ODYN: An All-Shifted Non-Interior-Point Method for Quadratic Programming in Robotics and AI

• URL: http://arxiv.org/abs/2602.16005v1
• Date: Tue, 17 Feb 2026 20:52:32 GMT
• Title: ODYN: An All-Shifted Non-Interior-Point Method for Quadratic Programming in Robotics and AI
• Authors: Jose Rojas, Aristotelis Papatheodorou, Sergi Martinez, Ioannis Havoutis, Carlos Mastalli,
• Abstract summary: ODYN is a novel all-shifted primal-dual non-interior-point quadratic programming solver.<n>It is designed to efficiently handle challenging dense and sparse QPs.<n>It exhibits strong warm-start performance and is well suited to both general-purpose optimization, and robotics and AI applications.
• Score: 6.322564456689471
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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