威尼斯人

Abstract: 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 (i.e., a matrix having unknown entries) such that the completed matrix is completely positive. We propose a semidefinite algorithm for solving general CP-completion problems, and study its properties. 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. Computational experiments are also presented to show how CP-completion problems can be solved.

简历：范金燕，上海交通大学威尼斯人 教授。2002年在中国科学院数学与系统科学研究院获理学博士学位。主要从事非线性最优化的理论和方法研究，在非线性方程组和完全正优化研究领域取得了一系列重要成果，相关论文发表在Math. Program.、SIAM J. Matrix Anal. Appl.、Math. Comp.等国际期刊上，并出版了专著《非线性方程组数值方法》。现为J. Ind. Manag. Optim.、J. Oper. Res. Soc. China、《计算数学》等学术期刊的编委。2017年荣获“第十三届中国青年女科学家奖”。