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

arXiv: https://arxiv.org/abs/2602.16005 · HTML: https://mlsanity.com/paper/2602.16005/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 70 references that are in the map.
- First posted on arXiv 17 Feb 2026.

## Builds on (most cited first, 18 of 18)

- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [OSQP: An Operator Splitting Solver for Quadratic Programs](https://mlsanity.com/paper/1711.08013/) (2017)
- [Accelerated Policy Learning with Parallel Differentiable Simulation](https://mlsanity.com/paper/2204.07137/) (2022)
- [gradSim: Differentiable simulation for system identification and visuomotor control](https://mlsanity.com/paper/2104.02646/) (2021)
- [Crocoddyl: An Efficient and Versatile Framework for Multi-Contact Optimal Control](https://mlsanity.com/paper/1909.04947/) (2019)
- [HPIPM: a high-performance quadratic programming framework for model predictive control](https://mlsanity.com/paper/2003.02547/) (2020)
- [GPU Acceleration of ADMM for Large-Scale Quadratic Programming](https://mlsanity.com/paper/1912.04263/) (2019)
- [Differentiation Through Black-Box Quadratic Programming Solvers](https://mlsanity.com/paper/2410.06324/) (2024)
- [PIQP: A Proximal Interior-Point Quadratic Programming Solver](https://mlsanity.com/paper/2304.00290/) (2023)
- [Non-Smooth Newton Methods for Deformable Multi-Body Dynamics](https://mlsanity.com/paper/1907.04587/) (2019)
- [Stability of Surface Contacts for Humanoid Robots: Closed-Form Formulae of the Contact Wrench Cone for Rectangular Support Areas](https://mlsanity.com/paper/1501.04719/) (2015)
- [A Feasibility-Driven Approach to Control-Limited DDP](https://mlsanity.com/paper/2010.00411/) (2020)
- [FBstab: A Stabilized Semismooth Quadratic Programming Algorithm with Applications in Model Predictive Control](https://mlsanity.com/paper/1901.04046/) (2019)
- [Inverse-Dynamics MPC via Nullspace Resolution](https://mlsanity.com/paper/2209.05375/) (2022)
- [Inverse Dynamics vs. Forward Dynamics in Direct Transcription Formulations for Trajectory Optimization](https://mlsanity.com/paper/2010.05359/) (2020)
- [Multi-Contact Inertial Parameters Estimation and Localization in Legged Robots](https://mlsanity.com/paper/2403.17161/) (2024)
- [A Non-Interior-Point Continuation Method for the Optimal Control Problem with Equilibrium Constraints](https://mlsanity.com/paper/2210.10336/) (2022)
- [Endpoint-Explicit Differential Dynamic Programming via Exact Resolution](https://mlsanity.com/paper/2503.03897/) (2025)

## Built on by (most cited first, 1 of 1)

- [Elastic ODYN: Differentiable Optimization for Infeasible Control and Learning in Robotics](https://mlsanity.com/paper/2606.16564/) (2026)

## Abstract (arXiv)

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-M'esz'aros 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).