ODYN: An All-Shifted Non-Interior-Point Method for Quadratic Programming in Robotics and AI
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910109919084544 |
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| author | Rojas, Jose Papatheodorou, Aristotelis Martinez, Sergi Patrizi, Andrea Havoutis, Ioannis Mastalli, Carlos |
| author_facet | Rojas, Jose Papatheodorou, Aristotelis Martinez, Sergi Patrizi, Andrea Havoutis, Ioannis Mastalli, Carlos |
| contents | 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). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_16005 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | ODYN: An All-Shifted Non-Interior-Point Method for Quadratic Programming in Robotics and AI Rojas, Jose Papatheodorou, Aristotelis Martinez, Sergi Patrizi, Andrea Havoutis, Ioannis Mastalli, Carlos Robotics Artificial Intelligence 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). |
| title | ODYN: An All-Shifted Non-Interior-Point Method for Quadratic Programming in Robotics and AI |
| topic | Robotics Artificial Intelligence |
| url | https://arxiv.org/abs/2602.16005 |