提出BC-ADMM优化器，加速机器人领域的非凸约束问题求解。
BC-ADMM: An Efficient Non-convex Constrained Optimizer with Robotic Applications
- 将非凸约束问题分解为可并行求解的小规模子问题，支持更大步长。
- 在四类机器人应用中，收敛速度比梯度下降和牛顿法更快。
- 理论与实践均保证渐近收敛性，适合实时控制场景。
非凸约束优化在多智能体导航、无人机轨迹规划和软体机器人模拟等机器人应用中普遍存在。传统优化器因步长过小导致收敛缓慢。本文提出一种改进的交替方向乘子法（BC-ADMM），通过双凸约束松弛处理一类非凸约束优化问题。该方法将原问题分解为多个易于并行求解的小规模子问题，从而允许更大的迭代步长。理论分析表明其具有收敛速度保障，实践中也表现出良好的渐近收敛性。在四类典型机器人应用的数值实验中，BC-ADMM在实际运行时间上显著优于传统梯度下降和牛顿法。
原文摘要 · Abstract (English)
Non-convex constrained optimizations are ubiquitous in robotic applications such as multi-agent navigation, UAV trajectory optimization, and soft robot simulation. For this problem class, conventional optimizers suffer from small step sizes and slow convergence. We propose BC-ADMM, a variant of Alternating Direction Method of Multiplier (ADMM), that can solve a class of non-convex constrained optimizations with biconvex constraint relaxation. Our algorithm allows larger step sizes by breaking the problem into small-scale sub-problems that can be easily solved in parallel. We show that our method has both theoretical convergence speed guarantees and practical convergence guarantees in the asymptotic sense. Through numerical experiments in a row of four robotic applications, we show that BC-ADMM has faster convergence than conventional gradient descent and Newton's method in terms of wall clock time.
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