Speaker: 凌舒扬 (上海纽约大学)
Time: 2025-12-18 15:00-16:00
Location: 1610, SIMIS
摘要：
The orthogonal group synchronization problem, which focuses on recovering orthogonal group elements from their corrupted pairwise measurements, encompasses examples such as high-dimensional Kuramoto model on general signed networks, $\mathbb{Z}_2$-synchronization, community detection under stochastic block models, and orthogonal Procrustes problem. The semidefinite relaxation (SDR) has proven its power in solving this problem; however, its expensive computational costs impede its widespread practical applications. We consider the Burer-Monteiro factorization approach to the orthogonal group synchronization, an effective and scalable low-rank factorization to solve large scale SDPs. Despite the significant empirical successes of this factorization approach, it is still a challenging task to understand when the nonconvex optimization landscape is benign, i.e., the optimization landscape possesses only one local minimizer, which is also global. In this work, we demonstrate that if the condition number of the Hessian at the global minimizer is small, the optimization landscape is absent of spurious local minima. Our main theorem is purely algebraic and versatile, and it seamlessly applies to all the aforementioned examples: the nonconvex landscape remains benign under almost identical condition that enables the success of the SDR. As a byproduct, we characterize the global synchronization of Kuramoto model on the expander graphs.
About Speaker:
凌舒扬现任职于上海纽约大学，是数据科学的长聘轨助理教授。在加入上海纽约大学之前，他于2017年至2019年在纽约大学柯朗数学研究所和数据科学研究所担任柯朗讲师。他在2017年6月从加州大学戴维斯分校应用数学专业获得博士学位。他的研究兴趣主要在数据科学、计算调和分析、优化和信号处理等，主要成果发表在如FOCM, MP, SIOPT, SIIMS, ACHA, IEEE-IT, JMLR, IP等杂志上。他主持2项国家自然科学基金和3项上海市科委/教委研究基金、参与国家重点研发计划青年科学家项目，并获得国家级青年人才计划、上海市以及浦东新区人才计划的支持。
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