报告题目 (Title)：The Rank-1Tensor Completion Problem（秩一张量补全问题）
报告人 (Speaker)：Jiawang Nie（University of California, San Diego）
报告时间 (Time)：2024年07月29日(周一) 10：00
报告地点 (Place)：校本部GJ403
邀请人(Inviter)：周安娃
主办部门：永利数学系
报告摘要： We discuss the rank-1 tensor completion problem for cubic order tensors. First of all, we show that this problem is equivalent to a special rank-1 matrix recovery problem. We propose both nuclear norm relaxation and moment relaxation methods for solving the resulting rank-1 matrix recovery problem. The nuclear norm relaxation sometimes get a rank- tensor completion, while sometimes it does not. When it fails, we apply the moment hierarchy of semidefinite programming relaxations to solve the rank- matrix recovery problem. The moment hierarchy can always get a rank- tensor completion, or detect its nonexistence. In particular, when the tensor is strongly rank-1 completable, we show that the problem is equivalent to a rank-1 matrix completion problem and it can be solved by an iterative formula. Therefore, much larger size problems can be solved efficiently for strongly rank-completable tensors. Numerical experiments are shown to demonstrate the efficiency of these proposed methods.
