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学术报告:The CP-matrix completion problem

 
报告题目The CP-matrix completion problem
报告时间201798日(周五)9:00-10:00
报告地点:西教五416(理学院)
报告人:范金燕

报告人简介:
       范金燕,上海交通大学数学科学学院教授。2002年在中国科学院数学与系统科学研究院获博士学位。先后访问英国剑桥大学和美国加州大学圣迭戈分校。主要从事非线性最优化的理论和方法研究,在非线性方程组的数值解法和完全正优化方面取得了一系列重要的成果,提出了非线性方程组的高阶Levenberg-Marquardt方法和信赖域半径趋于零的信赖域方法,解决了矩阵领域中的完全正填充问题和完全正分解问题。所指导博士获2016年全国博士后创新人才计划。2017年获第十三届中国青年女科学家奖。

 
报告摘要:
       A symmetric matrix $C$ is completely positive (CP) if there exists an entrywise nonnegative matrix $B$ such that $C="BB^T$." The CP-completion problem is to study whether we can assign values to the missing entries of a partial matrix such that the completed matrix is completely positive. In this talk, we propose a semidefinite algorithm for solving general CP-completion problems, and study its properties. When all the diagonal entries are given, the algorithm can give a certificate if a partial matrix is not CP-completable, and it almost always gives a CP-completion if it is CP-completable. When diagonal entries are partially given, similar properties hold. Computational experiments are also presented to show how CP-completion problems can be solved.

 

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