报告题目：Tensor Completion via A Generalized Transformed Tensor T-Product Decomposition without t-SVD
主讲人：凌晨教授（杭州电子科技大学）
时间：2026年5月14日（周四）15:00 p.m.
地点：北院卓远楼305贝斯特全球最奢华的游戏平台议室
主办单位：统计与数学ng28南宫
摘要：
Matrix and tensor nuclear norms have been successfully used to promote the low-rankness of tensors in low-rank tensor completion. However, singular value decomposition (SVD), which is computationally expensive for large-scale matrices, frequently appears in solving these nuclear norm minimization models. Based on the tensor-tensor product (T-product), in this talk, we first establish the equivalence between the so-called transformed tubal nuclear norm for a third order tensor and the minimum of the sum of two factor tensors’ squared Frobenius norms under a general invertible linear transform. Gainfully, we introduce a spatio-temporal regularized tensor completion model that is able to maximally preserve the hidden structures of tensors. Then, we propose an implementable alternating minimization algorithm to solve the underlying optimization model. It is remarkable that our approach does not require any SVDs and all subproblems of our algorithm have closed-form solutions. A series of numerical experiments on traffic data recovery, color images and videos inpainting demonstrate that our SVD-free approach takes less computing time to achieve satisfactory accuracy than some state-of-the-art tensor nuclear norm minimization approaches.
主讲人简介：
凌晨，杭州电子科技大学理ng28南宫（二级）教授，博士生导师。曾任：杭州电子科技大学理ng28南宫院长、中国运筹学贝斯特全球最奢华的游戏平台数学规划分贝斯特全球最奢华的游戏平台副理事长、中国经济数学与管理数学研究贝斯特全球最奢华的游戏平台副理事长、中国运筹学贝斯特全球最奢华的游戏平台理事、中国系统工程学贝斯特全球最奢华的游戏平台理事、浙江省数学贝斯特全球最奢华的游戏平台常务理事。现任：ESI期刊 Pacific Journal of Optimization编委、国际期刊Statistics, Optimization & Information Computing编委。研究方向：非线性规划、变分不等式与互补问题、张量计算、多变量多项式优化、半无限规划、随机规划、多目标优化理论与应用等。近十五年来，连续主持国家自科基金和浙江省自科基金各多项、其中省基金重点项目1项。在国内外重要刊物发表论文100余篇，其中SCI期刊论文90余篇，多篇发表在Math. Program.、SIAM J. on Optim.和 SIAM J.on Matrix Anal.and Appl. 、COAP、JOTA、JOGO等。
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