地点：维格堂319室
报告人：李仁仓教授（美国得克萨斯阿灵顿分校）
Part I
时间：7月13号（周四）上午11:00-12：00
地点：维格堂319室
报告人：李仁仓教授（美国得克萨斯阿灵顿分校）
Part II
Abstract
The NEPv approach has been increasingly used lately for optimization on the Stiefel manifold arising from machine learning. General speaking, the approach first turns the first order optimality condition into a nonlinear eigenvalue problem with eigenvector de- pendency (NEPv) and then solve the nonlinear problem via some variations of the self- consistent-field (SCF) iteration. The difficulty, however, lies in designing a proper SCF iteration so that a maximizer is found at the end. Currently, each use of the approach is very much individualized, especially in its convergence analysis to show that the approach does work or otherwise. Related, the NPDo approach is recently proposed for the sum of coupled traces and it seeks to turn the first order optimality condition into a nonlinear polar decomposition with orthogonal factor dependency (NPDo).
This talk consists of two parts, approximately one hour each. Part I is about a unifying framework for the NPDo approach, while Part II about a unifying framework for the NEPV approach. The frameworks are built upon some basic assumptions, with which globally convergence to a stationary point is guaranteed and during the SCF iterative process that leads to the stationary point, the objective function increases monotonically. Also notion of atomic function is proposed, which include commonly used matrix traces of linear and quadratic forms as special ones. It is shown that the basic assumptions are satisfied by atomic functions and, more importantly, by convex compositions of the atomic functions. Together they provide a large collection of objectives for which the NEPv approach and the NPDo approach are guaranteed to work.
邀请人：张雷洪