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The CP-matrix completion problem


Academic Report

Title: The CP-matrix completion problem

Reporter: Prof. FAN Jinyan (College of mathematics and science, Shanghai Jiao Tong University)

Time: June 11, 2018 (Monday) PM 15:30-16:30

Location: 407# room, Graduate Teaching Building

Contact: Prof. ZHANG Liwei (tel:84708351-8118)

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.

The brief introduction to the reporter: Fan Jinyan, Professor of College of Mathematics and Science, Shanghai Jiao Tong University. In 2002, she received her doctorate in science from the Institute of mathematics and systems science, Chinese Academy of Sciences. She is mainly engaged in the study of the theory and method of nonlinear optimization and has made a series of important achievements in the field of nonlinear equations and fully positive optimization. The related papers are published in "Math. Program.", "SIAM J. Matrix Anal. Appl.", "Math. Comp." and other international journals, and she published the monograph "The numerical method of nonlinear equations". She is now the editorial board of academic journals such as "J. Ind. Manag. Optim.", "J. Oper. Res. Soc. China" and computational mathematics. She was awarded the thirteenth China young women Scientist Award in 2017.