Decentralized Optimization Over the Stiefel Manifold by an Approximate Augmented Lagrangian Function
报告专家：刘歆 研究员（中国科学院数学与系统科学研究院）
报告时间：9月23日星期五下午2：00-3：00
报告地点：腾讯会议：507-829-789
摘要：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.
专家简介：刘歆，2004年本科毕业于北京大学数学科学学院，2009年于中国科学院数学与系统科学研究院获得理学博士学位。现为中国科学院数学与系统科学研究院研究员、博士生导师，2022年1月被聘为“冯康首席研究员”。主要研究方向为非线性优化的计算方法。刘歆于2016年获得国家优秀青年科学基金，2021年获得国家杰出青年科学基金。现为中国科学院数学与系统科学研究院-香港理工大学“应用数学”联合实验室副主任，中国运筹学会常务理事，中国工业与应用数学会副秘书长；Mathematical Programming Computation, Journal of Computational Mathematics, Journal of Industrial and Management Optimization, Asia-Pacific Journal of Operational Research,《运筹学通讯》等国内外期刊编委。
