报告人: 谢资清（湖南师范大学）

报告人简介: 谢资清，湖南师范大学sunbet中国官网教授、博士生导师、院长，“计算与随机数学”教育部重点实验室主任，第十三届全国人大代表。现任中国数学会理事、中国工业与应用数学会理事、湖南省计算数学与应用软件学会理事长、湖南省数学会副理事长,教育部本科教学审核评估专家，国家自然科学基金委会评专家。1996年毕业于中国科学院应用数学研究所，师从丁夏畦院士，获理学博士学位。2012年以第一完成人身份获湖南省自然科学奖一等奖。2006年入选教育部新世纪优秀人才培养计划，2014年获批为享受国务院政府特殊津贴专家，入选2018年度湖南省优秀师德典型。主持国家自然科学基金项目8项，其中重大研究计划项目1项。主要从事计算数学与应用数学的研究工作。曾多次应邀访问美国、瑞典、德国、日本、俄罗斯、新加坡、香港、捷克、挪威等国家和地区的知名大学。

报告（一）

报告题目：A Globally Convergent Barzilai-Borwein-type Local Minimax Method for Finding Multiple Saddle Points

报告摘要：Saddle points, which are unstable critical points, have a widely range of applications in many fields of nonlinear science, such as nonlinear optics, condensed matter physics, chemical reactions, and materials science etc.. Owning to the nonlinearity of model problems, the multiplicity and instability of saddle points, it is extremely challenging to design a stable, efficient and globally convergent numerical algorithm for finding saddle points. In this talk, a globally convergent Barzilai-Borwein-type local minimax method (GBB-LMM) is proposed for finding multiple saddle points of nonconvex functionals in Hilbert space, where the idea of the Barzilai-Borwein gradient method combining with the nonmonotone line search strategy in optimization in Euclidean space is applied to solve a two-level local optimization problem. Actually, the Barzilai-Borwein-type step-size is explicitly constructed as a trial step-size at each iteration step of the local minimax method, and the nonmonotone step-size search rule is introduced to guarantee the global convergence. The feasibility and global convergence of the GBB-LMM are rigorously verified. The GBB-LMM is then implemented to solve several typical nonlinear boundary value problems with variational structures for multiple unstable solutions. The numerical results indicate that our approach may greatly speed up the convergence of traditional local minimax methods.

报告时间: 2019年4月27日（星期六）下午3:00-4:00.

报告地点: 科技楼南楼702室

报告（二）

报告题目：Two Methods for Finding Multiple Solutions of Semilinear PDEs

报告摘要：In this talk, wepresenttwo approaches for finding the multiple solutions of semilinear PDEs. The first one is theNormalized Goldstein-type Local Minimax Method (NG-LMM) which is aimed to find multiple minimax-type solutions with variational structures. The second one is the Augmented Partial Newton Method (APNM) which is devoted to find multiple minimax-type solutions of semilinear PDEs no matter whether they are variatioal or not. More significantly, these two approaches are large-scope algorithms. The corresponding theoretical analysis is provided also.

报告时间: 2019年4月27日（星期六）下午4:10-5:10.

报告地点: 科技楼南楼702室