学者论坛:变分不等式理论与应用

文:教师发展中心 / 来源:人力资源部 / 2016-12-23 / 点击量:1065

  人力资源部教师发展中心开展“学者论坛”系列活动,定期邀请国内外知名专家学者、国家级教学名师等作专题报告,旨在加强广大师生的学术思想交流和碰撞,促进青年教师成长,开拓学生视野。现将第46期论坛安排如下,欢迎广大师生参加。

  一、时 间:2016年12月24日 (周六)上午10:00

  二、地 点:清水河校区主楼A1-512

  三、主题一:A Class of Differential Inverse Variational Inequalities in Finite Dimensional Spaces

  主讲人:黄南京 (2015 年Elsevier中国高被引学者、四川大学教授)

  交流内容:

  In this paper, a new differential inverse variational inequality is introduced and Studied in finite dimensional Euclidean spaces. Some results concerned with the linear growth of the solution set for the differential inverse variational inequalities are obtained under different conditions. Some existence theorems of Carath´eodory weak solutions for the differential inverse variational inequality are also established under suitable conditions. An application to the time-dependent spatial price equilibrium control problem is also given.  This is a joint work with W. Li and X. Wang. 

  主讲人简介:

  黄南京教授是四川大学二级教授,博士生导师,四川省学术带头人,第二届四川省专家评议(审)委员会成员,中国运筹学会常务理事。主持过国家自然科学基金和教育部基金项目多项,在变分不等式理论和相补问题、向量优化、集值分析、均衡问题的理论和算法及其应用、微分变分不等式以及金融优化等方面的研究成果丰富, 在国内外知名的学术刊物发表SCI收录论文多篇,2014年和2015年入选Elsevier中国高引文学者。相关研究成果曾获得教育部自然科学奖“一等奖”和教育部科技进步奖“一等奖”。

  四、主题二:Dual variational inequality

  主讲人:何诣然 (四川师范大学教授)

  交流内容:

  Dual variational inequality is an important tool in the study of variational inequality, especially when the mapping involved has a certain monotonicity. Unlike the variational inequality, the dual variational inequality requires more assumptions for the existence of solutions. In this talk, we recall some main results on the existence of solutions of dual variational inequality, analyze its relationship with monotonicity, and propose some possible problems.

  主讲人简介:

  何诣然教授于2001年在香港中文大学数学系获博士学位,现为四川师范大学科研处处长、博士生导师。先后应邀访问新加坡国立大学、香港理工大学、香港中文大学等知名高校。

  何诣然教授于2005年被批准为四川省学术与技术带头人后备人选,2006年被评为四川师范大学基础数学专业首批博士生导师,2009年入选中组部“西部之光”计划,2011年获全国五一劳动奖章,2015年1月评为四川省有突出贡献的优秀专家,2015年4月评为全国先进工作者。主要研究方向为非线性最优化,先后主持国家自然科学基金项目(3项)、四川省青年科技基金项目等多项省部级科研项目。

  五、主题三:Near convexity and near equality of functions and applications

  主讲人:李军 (西华师范大学教授,数学与信息学院副院长)

  流内容:

  In this talk, we investigate near equality and near convexity of extended real valued functions defined on finite-dimensional Euclidean spaces. The main result states that a nearly convex function (respectively, its domain, lower level set) is nearly equal (respectively, the domain, lower level set of) its closure, convex hull and closed convex hull. Near convexity of a extended real function is proved to equal near equality of itself and another nearly convex function under the assumption that the convex function involved majorizes itself. It is shown that the operations on sum, scalar multiple, epi-sum, epi-multiple and pointwise supremum of nearly convex functions are also true under mild assumptions, and proximal average of nearly convex functions enjoys many nice properties of that of lower semi-continuous and convex functions obtained by Bauschke, Lucet and Trienis. As applications, the solution set of nearly convex optimization problems is proved to be nearly convex, the solution sets of two nearly convex optimization problems are shown to be nearly equal if the two nearly convex functions involved do and moreover, the Fenchel duality theorem is proved to hold for nearly convex optimization problems.

  主讲人简介:

  李军教授是西华师范大学数学与信息学院副院长,四川省学术与技术带头人,主要从事最优化理论与方法等方面的研究工作。在Sci. China Math., Europen J. Oper. Res.,J. Optim. Theory Appl., J. Global Optim., Optim.等杂志上发表学术论文三十余篇。主持过国家自然科学基金面上项目、青年基金项目,教育部科学技术重点项目和四川省青年科技基金项目。

  六、主持人:数学科学学院 肖义彬副教授

  七、主办单位:人力资源部教师发展中心

    承办单位:数学科学学院


                人力资源部教师发展中心

                  2016年12月23日


编辑:林坤  / 审核:林坤  / 发布者:林坤