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Graduate Student Seminar


Biological Sciences : 120

Date & Time

February 26, 2014, 11:00 am12:00 pm


SpeakerJuyoung Jeong
Session ChairZois Boukouvalas
DiscussantDr. Potra
PlaceBS 120
Convex cones of matrices
Convex cones of matrices—especially positive semidefinite (PSD) matrices, doubly nonnegative (DNN) matrices, or completely positive (CP) matrices— and its dual cone arise in several areas of applied mathematics, including optimization. We say a convex cone K is pointed if the intersection of K and –K is only the zero set, and K is solid if its interior is nonempty. If a convex cone K is closed, pointed, and solid, then K is said to be a full cone. We: (i) show that PSD, DNN, CP are all full cones; (ii) demonstrate their duals explicitly; and (iii) investigate the difference between DNN and CP.