学术报告报告题目1：Repeation invariant geometric means
报告人：Yongdo Lim 教授（Sungkyunkwan University）
报告时间：2017年8月22日上午10:00-11:00
报告题目2：GRADIENT PROJECTION METHODS FOR THE N-COUPLING PROBLEM
报告人： Sangho Kum 教授（Chungbuk National University）
报告时间：2017年8月22日上午11:00-12:00
报告地点：4号楼4224室。
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报告1摘要： We present a new construction scheme of multivariate geometric means of positive definite matrices. This new family of multivariate geometric means retains most important properties of the Cartan mean, the least squares mean from the Riemannian trace metric on the cone of positive definite matrices. Appropriate versions of the Karcher equation, Yamazaki's inequality, and the unitarily invariant norm inequality are presented.
报告2摘要：We are concerned with optimization methods for the L2-Wasserstein least squares problem of Gaussian measures (alternatively the n-coupling problem). Based on its equivalent form on the convex cone of positive definite matrices of fixed size and the strict convexity of the variance function, we are able to present a successful optimization algorithm for the unique minimizer. Its global convergence rate analysis is provided according to the derived upper bound of Lipschitz constants of the gradient function.