• 论文 •

### 低秩张量填充的加速随机临近梯度算法

1. 工程科学计算山西省高等学校重点实验室(太原师范学院), 晋中 030619
• 收稿日期:2021-05-10 出版日期:2022-11-14 发布日期:2022-11-08
• 通讯作者: 王川龙,Email:clwang1964@163.com.
• 基金资助:
国家自然科学基金（11371275），山西省自然科学基金（201601D011004），山西省研究生教育创新项目（2021Y713）和太原师范学院研究生教育创新项目（SYYJSJC-2164）资助.

Guo Xiongwei, Wang Chuanlong. AN ACCELERATED STOCHASTIC PROXIMAL GRADIENT ALGORITHM FOR LOW RANK TENSOR COMPLETION[J]. Mathematica Numerica Sinica, 2022, 44(4): 534-544.

### AN ACCELERATED STOCHASTIC PROXIMAL GRADIENT ALGORITHM FOR LOW RANK TENSOR COMPLETION

Guo Xiongwei, Wang Chuanlong

1. Key Laboratory of Engineering and Computational Science (Taiyuan Normal University), Shanxi Province Department of Education, Jinzhong 030619, China
• Received:2021-05-10 Online:2022-11-14 Published:2022-11-08

In this paper, an accelerated stochastic proximal gradient algorithm is proposed for low rank tensor completion problem. The tensor completion model is relaxed into an unconstrained optimization problem in the form of average combination. In the iterative process, a function of this combination is randomly selected for variable update, which effectively reduces the large calculation cost caused by tensor unfolding, matrix folding, and singular value decomposition. We prove that the convergence rate of this algorithm is $O(1/k^{2})$. Finally, numerical results on randomly generated and real tensor completion problems demonstrate new algorithm is better than three existing algorithms in CPU time.

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