报告题目：Copositivity Detection of Tensors: Theory and Algorithm

报告人：黄正海（天津大学）

时间：2016-05-14

地点：数学院一楼报告厅

摘要： A symmetric tensor is called copositive if it generates a multivariate form taking nonnegative values over the nonnegative orthant. Copositive tensors have found important applications in polynomial optimization and tensor complementarity problems. In this talk, we consider copositivity detection of tensors both from theoretical and computational points of view. After giving several necessary conditions for copositive tensors, we propose several new criteria for copositive tensors based on the representation of the multivariate form in barycentric coordinates with respect to the standard simplex and simplicial partitions. It is verified that, as the partition gets finer and finer, the concerned conditions eventually capture all strictly copositive tensors. Based on the obtained theoretical results with the help of simplicial partitions, we propose a numerical method to judge whether a tensor is copositive or not. The preliminary numerical results confirm our theoretical findings.

报告时间：5月14日下午3点

报告人简介：

黄正海，天津大学理学院数学系，教授，博士生导师,系主任。中国数学会理事、中国运筹学会理事、中国计算学学会理事；天津市数学会副理事长、天津市运筹学会副理事长、天津市计算数学学会副理事长、天津市工业与应用数学会副理事长。博士毕业于复旦大学统计运筹系。研究方向：最优化理论方法及应用。主持国家自然科学基金等基金项目10余项，发表SCI检索论文70余篇。曾获中科院优秀博士后奖、教育部高等学校自然科学奖二等奖。担任国际期刊《Applied Mathematics and Computation》和《Optimization,Statistics & Information Computing》的编委、中国核心期刊《运筹学学报》的编委。