数学与统计学院报告会

腾 讯 ID：743-687-844

主办单位：数学与统计学院

欢迎光临！

报告1：

报告题目：Stochastic splitting algorithms for nonconvex problems in imaging and data sciences

主 讲 人：张小群 上海交通大学 教授

时    间：8月12日9:00

摘    要：Splitting algorithms are largely adopted for composited optimization problems arising in imaging and data sciences. In this talk, I will present stochastic variants of composited optimization algorithms in nonconvex settings and their applications. The first class of algorithms is based on Alternating direction method of multipliers (ADMM) for nonconvex composite problems. In particular, we study the ADMM method combined with a class of variance reduction gradient estimators and established the global convergence of the sequence and convergence rate under the assumption of Kurdyka-Lojasiewicz (KL) function. The efficiency of the algorithms is verified through statistical learning examples and L0 based sparse regularization for 3D image reconstruction. The second class of stochastic algorithm is proposed for a type of three-block alternating minimization arising in training quantized neural networks.  We develop a convergence theory for the stochastic three-block algorithm (STAM) and obtain an -stationary point with optimal convergence rate . The experiments on training quantized DNNs are carried out on different network structures on CIFAR-10 and CIFAR-100 datasets. The test accuracy indicates the effectiveness of STAM algorithm for training binary quantization DNNs.

专家简介：张小群, 上海交通大学自然科学研究院和数学科学学院特聘教授。主要研究方向：图像科学、医学图像处理、数据科学等问题中的数学模型与计算方法。现任Inverse problems and Imaging、 CSIAM-AM杂志编委，CSIAM数学大数据与人工智能专委会、数学与医学交叉学科专业委员会委员。

报告2：

报告题目：Second-order geometric quasilinear hyperbolic partial differential equations and their applications

主 讲 人：董国志  中南大学

时    间：8月12日10:00

摘    要：I will introduce a class of second-order quasilinear hyperbolic PDEs which are motivated from recent advances of second-order dynamics in convex optimization and applications in mathematical imaging. They are second-order counterparts of the total variation flow and the mean curvature flow for level sets of scalar functions. Analytical results as well as some numerical behavior of solutions will be presented. Some open issues and potential extensions will be discussed as well.

专家简介：

董国志，2022-现在 中南大学特聘副教授

2019-2022 柏林洪堡大学/魏尔斯特拉斯研究所助理研究员

2017-2019柏林洪堡大学博士后/科研助理（导师 Michael Hintermueller）

2012-2017维也纳大学博士生/科研助理（导师 Otmar Scherzer）

2010-2011 东芬兰大学硕士研究生（欧盟教育委员会资助）

2009-2012 湖南师范大学硕士研究生（导师谢资清）

2007-2012 湖南师范大学科研与研究生工作秘书

2003-2007 湖南师范大学本科