completely positive matrices, copositive matrices, doubly nonnegative matrices, extremal matrices, copositive optimization
We describe the main open problems which are currently of interest in the theory of copositive and completely positive matrices. We give motivation as to why these questions are relevant and provide a brief description of the state of the art in each open problem.
Berman, Avi; Dur, Mirjam; and Shaked-Monderer, Naomi.
"Open problems in the theory of completely positive and copositive matrices",
Electronic Journal of Linear Algebra,
Volume 29, pp. 46-58.