报告题目 (Title)：Robust Completion for Rank-1 Tensors with Noises（带噪声的秩一张量鲁棒填充问题）
报告人 (Speaker)：聂家旺 教授（加州大学圣地亚哥分校）
报告时间 (Time)：2025年07月3日（周四）9：00
报告地点 (Place)：#腾讯会议1：348-834-291
#腾讯会议2：413-253-367
邀请人(Inviter)：周安娃
主办部门：8455新葡萄场网站数学系
报告摘要： We discuss the rank-1 tensor completion problem for cubic tensors when there are noises for observed tensor entries. First, we propose a robust biquadratic optimization model for obtaining rank-1 completing tensors. When the observed tensor is sufficiently close to be rank-1, we show that this biquadratic optimization produces an accurate rank-1 tensor completion. Second, we give an efficient convex relaxation for solving the biquadratic optimization. When the optimizer matrix is separable, we show how to get optimizers for the biquadratic optimization and how to compute the rank-1 completing tensor. When that matrix is not separable, we apply its spectral decomposition to obtain an approximate rank-1 completing tensor. Numerical experiments are given to explore the efficiency of this biquadratic optimization model and the proposed convex relaxation.
