Matrix theory is one of the most fundamental tools of mathematics and science, and a
number of classical books on matrix analysis have been written to explore this theory. As a …

A real matrix is positive semidefinite if it can be decomposed as A= BB′. In some
applications the matrix B has to be elementwise nonnegative. If such a matrix exists, A is …

Copositive programming is a relatively young field in mathematical optimization. It can be
seen as a generalization of semidefinite programming, since it means optimizing over the …

A standard quadratic problem consists of finding global maximizers of a quadratic form over
the standard simplex. In this paper, the usual semidefinite programming relaxation is …

Copositive programming has become a useful tool in dealing with all sorts of optimisation
problems. It has however been shown by Murty and Kabadi (Math. Program. 39 (2): 117 …

In every single second in this modern era, tons of data are being generated. Think of the
number of online people writing their blogs, designing their homepages and sharing their …

Extracting low-rank and sparse structures from matrices has been extensively studied in
machine learning, compressed sensing, and conventional signal processing, and has been …

Nonnegative matrix factorization (NMF) has been greatly popularized by its parts-based
interpretation and the effective multiplicative updating rule for searching local solutions. In …

Nonnegative tensor factorization has applications in statistics, computer vision, exploratory
multiway data analysis, and blind source separation. A symmetric nonnegative tensor, which …

An n-by-n symmetric matrix A is called doubly nonnegative (DN) if A is entry-wise
nonnegative (4 2 0) and positive semidefinite (psd). An n-by-n symmetric matrix A is called …