报告时间：2021年5月1日（周六）8:30 -- 11:30

报告地点：主楼124房间理学院会议室

主办单位：理学院

报告题目一：Smoothing fast iterative hard thresholding algorithm for L0 regularized nonsmooth convex regression problem

报告人：边伟 教授

报告人单位：哈尔滨工业大学数学学院

时间：8：30-9：15

报告摘要：In this talk, I first introduce a class of constrained sparse regression problem with cardinality penalty, where the feasible set is box constraint, and the loss function is convex, not differentiable. I put forward a smoothing fast iterative hard thresholding (SFIHT) algorithm for solving such optimization problems, which combines smoothing approximations, extrapolation techniques and iterative hard thresholding methods. The extrapolation coefficients satisfy in the proposed algorithm. Any accumulated point of the iterative sequence is a local minimizer of the original cardinality penalty problem. We then consider that the case where the loss function is differentiable. We propose the fast iterative hard thresholding (FIHT) algorithm to solve such problems. We prove that the iterates converges to a local minimizer with lower bound property of the problem. In particular, we show that the convergence rate of the corresponding objective function value sequence is . Finally, we perform some numerical examples to illustrate the theoretical results.

报告人简介：边伟，哈尔滨工业大学数学学院，教授、博士生导师，数学研究院双聘人员。2004年和2009年于哈尔滨工业大学分别获得学士和博士学位，导师为薛小平教授，随后留校工作至今。期间，2010-2012年访问香港理工大学跟随陈小君教授，从事博士后工作。现任黑龙江省数学会常务理事，中国运筹学会理事，中国运筹学会数学规划分会理事. 主要研究方向为非光滑优化问题的理论与算法研究，已在 MP, SIOPT, SIIMS, SINUA，MOR和三个IEEE系列汇刊发表多篇学术论文。

报告题目二：Recent Progress on Some Elliptic and Parabolic Equations

报告人：张超 教授

报告人单位：哈尔滨工业大学数学学院

时间：9：15-10：00

报告摘要：In this talk, we first review some regularity results for the gradient of solutions of nonlinear elliptic equations with unbalanced growth. Then we present a result on the equivalence between weak solutions and viscosity solutions for double-phase equations. Moreover, we report a new Campanato type estimate for the weak solutions of multi-phase equations. The result obtained here is different from the BMO type estimates for the usual p- Laplacian equation due to DiBenedetto and Manfredi. The content of this talk is in close relationship with the recent pioneering contributions of Marcellini and Mingione in the qualitative analysis of double phase problems.

报告人简介：张超，哈尔滨工业大学数学学院和数学研究院教授，博士生导师，主要从事非线性椭圆和抛物型偏微分方程的适定性、正则性和渐近行为等方面的研究。在JFA, CVPDE, IUMJ, JDE等杂志上发表40余篇高水平SCI论文，担任国际SCI期刊《Advances in Nonlinear Analysis》编委。

报告题目三：A study on the Kuramoto type oscillators

报告人：李祝春 教授

报告人单位：哈尔滨工业大学数学学院

时间：10：00-10：45

报告摘要：We continue the study of the Hebbian network of Kuramoto oscillators with a second-order Fourier term with the purpose to apply the system to the binary retrieve task with nonorthogonal standard binary patterns. In [SIAM J. Appl. Dyn. Syst. 19 (2020) 1124-1159] the authors considered the system and introduced the so-called $\varepsilon$-independent stability which means that the concerned equilibria, typically the memorized binary patterns, are stable for any $\varepsilon>0$. The key idea was to memorize those mutually orthogonal binary patterns in the network and one of them should be retrieved for a given defective

pattern. However, in practice the orthogonality usually fails. When the orthogonality in the standard patterns fails, in this paper we propose a new strategy which transfers the problem to a case with orthogonality and the standard patterns are $\varepsilon$-independentlysymptotically stable. Numerical simulations are provided to illustrate the approach.

报告人简介：李祝春，哈尔滨工业大学数学学院教授、博士生导师，数学研究院双聘人员。毕业于哈尔滨工业大学，分别于2005年和2011年获得学士和博士学位，导师为薛小平教授。2011年留校工作，期间于2011年至2013年赴首尔国立大学数学科学系做博士后，合作导师为ICM邀请报告人Ha Seung-Yeal教授。主要从事多个体耦合系统集群行为及其应用研究，已在SIAP, SICON, SIADS, M3AS，Nonlinearity, JDE等刊物发表论文30余篇，是美国数学会数学评论评论员，德国数学文摘评论员，担任JDE, Nonlieanrity, Physica D, IEEE Trans等期刊的审稿人。

报告题目四：A sub-gradient neural network for nonconvex and interval quadratic programming problems

报告人：刘凤秋 教授

报告人单位：宁波工程学院理学院

时间：10：45-11:30

报告摘要：This study focuses on the nonconvex and interval quadratic programming problem based on subgradient-based on neural network algorithm, and further investigate the convergent rate of optimal solutions by using the Lojasiewicz inequality. The weight parameters are first regarded as the decision variables in the nonconvex and interval quadratic programming problems. In actual applications, the determination of weights are not easy obtained. Compared to the given weights, the proposed algorithm can obtain the optimal solutions. The neural network algorithm is first used to solve the nonconvex and cubic programming problems. The nonconvex and interval quadratic programming problems are converted into a nonconvex and cubic programming problems by the nonnegative of decision variables and the parameter representation of intervals.

报告人简介：刘凤秋，博士，教授。分别在东北师范大学、哈尔滨工业大学、哈尔滨工业大学分别获学士、硕士和博士学位。现为宁波工程学院理学院教师、数据科学与大数据技术专业负责人。近年来，主要从事数据挖掘、机器学习中的支持向量机、神经网络优化等研究与应用。主持或参加各类科研项目8项，其中主持国家自然科学基金项目1项，主持省自然科学基金项目1项，教育厅科学基金项目1项，横向课题1项。