学术报告

题      目：Tensor Completion  via  Minimin and Minimax Optimization with the Smooth $\varepsilon$-Trace Function

报  告  人：王川龙  教授  (邀请人：黎稳 )

                                  太原师范学院

时      间：1月4日  17：00-18：00

腾讯会议：807-639-333   

报告人简介:

        王川龙，男，教授，博士，博士生导师，山西省教学名师，山西省委联系的高级专家。曾任全国工业与应用数学学会常务理事、现任山西省工业与应用数学学会理事长。被评为山西省跨世纪学术和技术带头人、山西省科技进步二等奖、山西省自然科学奖二等奖、山西省教学成果一等奖等。主持国家自然科学基金委、省级项目十余项，在国内外学术期刊发表论文100余篇，SCI收录50余篇。

摘      要：

       In this paper, the  novel optimization models for tensor completion are proposed by considering the minimin and the minimax optimization models with the smooth $\varepsilon$-trace functions instead of nuclear norm,  and the minimin function in the new models is a non-convex and non-smooth function. The null space property condition and the restricted isometry constant are explored for low-rank tensors within these models. The optimality conditions of new optimization models and the relation with the restricted isometry property are studied. The objective function in the minimin and the minimax combination model is proved to be the Kurdyka-Lojasiewicz function with exponent $\frac{1}{2}$. Based on  Kurdyka-Lojasiewicz  property, the convergence theory of the augmented Lagrange multiplier method  is established by parameter adjustment for the new non-convex and non-smooth optimization model. It is also  proved that the sequence generated by the augmented Lagrange multiplier method converges to the locally optimal solution. Finally, extensive experimental results show that the minimin and the minimax combination model usually takes less than CPU time and gets better precision than the traditional nuclear norm-based model.

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