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The difference between 5x5 doubly nonnegative<br/><br/>and completely positive matrices<br/><br/><br/><br/>

Tuesday, November 18, 2008 - 10:30am - 11:15am
EE/CS 3-180
Kurt Anstreicher (The University of Iowa)
The convex cone of n×n completely positive (CPP) matrices
and its dual cone of copositive matrices arise in several
areas of applied mathematics, including optimization. Every
CPP matrix is doubly nonnegative (DNN), i.e., positive
semidefinite and component-wise nonnegative. Moreover
for n less than 5, every DNN matrix is CPP. We investigate the
difference between 5×5 DNN and CPP matrices. We give
a precise characterization of how a 5×5 DNN matrix that is
not CPP differs from a DNN matrix, and use this
characterization
to show how to separate an extreme DNN matrix
that is not CPP from the cone of CPP matrices.

Joint work with Sam Burer and Mirjam Duer.
MSC Code: 
47L07
Keywords: