报告题目：Decentralized Optimization Over the Stiefel Manifold by an Approximate Augmented Lagrangian Function

报告时间：2022-05-11  10:00 - 11:00

报告人：刘歆 研究员 中科院数学与系统科学研究院

腾讯会议ID：151-105-460

Abstract: We study the decentralized optimization problem over the Stiefel manifold, which is defined on a connected network of d agents. The objective is an average of d local functions, and each function is privately held by an agent and encodes its data. The agents can only communicate with their neighbors in a collaborative effort to solve this problem. In existing methods, multiple rounds of communications are required to guarantee the convergence, giving rise to high communication costs. In contrast, this paper proposes a decentralized algorithm, called DESTINY, which only invokes a single round of communications per iteration. DESTINY combines gradient tracking techniques with a novel approximate augmented Lagrangian function. The global convergence to stationary points is rigorously established. Comprehensive numerical experiments demonstrate that DESTINY has a strong potential to deliver a cutting-edge performance in solving a variety of testing problems.