# GPU Accelerated Convex Approximations for Fast Multi-Agent Trajectory Optimization

arXiv: https://arxiv.org/abs/2011.04240 · HTML: https://mlsanity.com/paper/2011.04240/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Nov 2020.

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

- [Flow-Opt: Scalable Centralized Multi-Robot Trajectory Optimization with Flow Matching and Differentiable Optimization](https://mlsanity.com/paper/2510.09204/) (2025)

## Abstract (arXiv)

In this paper, we present a computationally efficient trajectory optimizer that can exploit GPUs to jointly compute trajectories of tens of agents in under a second. At the heart of our optimizer is a novel reformulation of the non-convex collision avoidance constraints that reduces the core computation in each iteration to that of solving a large scale, convex, unconstrained Quadratic Program (QP). We also show that the matrix factorization/inverse computation associated with the QP needs to be done only once and can be done offline for a given number of agents. This further simplifies the solution process, effectively reducing it to a problem of evaluating a few matrix-vector products. Moreover, for a large number of agents, this computation can be trivially accelerated on GPUs using existing off-the-shelf libraries. We validate our optimizer's performance on challenging benchmarks and show substantial improvement over state of the art in computation time and trajectory quality.