报告题目：Decentralized Optimization Over the Stiefel Manifold by an Approximate Augmented Lagrangian Function
报告摘要：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.
报告时间：2024年4月20日下午
报告地点：启智楼80602会议室
个人简介：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博士学位。毕业后在中国科学院数学与系统科学研究院工作，2020年晋职为正研究员，2022年被聘为“冯康首席研究员”。主要研究方向包括：流形优化、分布式优化、统计大数据分析、材料计算、机器学习等。刘歆于2016年获得国家优秀青年科学基金；2016年获得中国运筹学会青年科技奖；2020年获得中国工业与应用数学学会应用数学青年科技奖；2021年获得国家杰出青年科学基金。现担任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，中国青年科技工作者协会理事，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 & Management Optimization》等国内外期刊编委。
