Convergence Analysis of ADMM for Multi-Affine Trajectory Optimization

Yutong Chao, Michal Ciebielski, Jalal Etesami, Majid Khadiv

Keywords: Nonconvex Optimization, Robot Locomotion

Abstract: In this paper, we study a class of non-convex optimization problems known as multi-affine quadratic equality constrained problems, which appear in various applications--from generating feasible force trajectories in robotic locomotion and manipulation to training neural networks. Although these problems are generally non-convex, they exhibit convexity or related properties when all variables except one are fixed. Under mild assumptions, we prove that the alternating direction method of multipliers (ADMM) converges when applied to this class of problems. Furthermore, when the ``degree'' of non-convexity in the constraints remains within certain bounds, we show that ADMM achieves a linear convergence rate. We validate our theoretical results through practical examples in robotic locomotion.

Submission Number: 15