报告人：Wotao Yin, University of California, Los Angeles, USA

报告题目：Block multi-convex optimization and its applications to matrix/tensor decomposition

报告地点：管理科研楼1518

报告时间：2013年7月13日星期六  上午10:00

Abstract: This talk considers block multi-convex optimization, where the feasible set and objective function are generally non-convex but convex in each block of variables. It also considers non-convex blocks and though requires these blocks to be processed by proximal minimization. After reviewing some interesting applications such as blind source separation, sparse dictionary learning, nonnegative matrix and tensor factorization, and low-rank matrix and tensor recovery, we propose a generalized block coordinate update method. While non-convex and/or nonsmooth functions can generally fail a block coordinate descent method, we establish the global convergence and asymptotic rate of convergence for our method applied to block multi-convex problems with separable nonsmooth terms. The analysis is based establishing the Kurdyka-Lojasiewicz inequality. We give a few large classes of functions that meet our assumptions. We present numerical results including nonnegative matrix and tensor decomposition.
  This is joint work with Yangyang Xu.

主办单位: 365英国上市官网  国家数学与交叉科学中心合肥分中心

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