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

TL;DR

ODYN is a new all-shifted primal-dual QP solver that efficiently handles dense and sparse problems, excelling in robotics and AI applications with strong warm-starting and real-time performance.

Contribution

It introduces a novel all-shifted NCP function combined with proximal methods, enabling robust, efficient, and versatile QP solving without linear independence constraints.

Findings

Demonstrates state-of-the-art convergence on benchmark tests.

Shows superior warm-starting capabilities in sequential problems.

Successfully deployed in control, learning, and simulation frameworks.

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-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).