Optimization, Algebra, and Geometry Seminar
— 3:30pm
Location:
Virtual Presentation - ET
-
Remote Access - Zoom
Speaker:
GABOR PATAKI
,
Professor, Department of Statistics & Operations Research, University of North Carolina at Chapel Hill
https://gaborpataki.web.unc.edu/
How do exponential size solutions arise in semidefinite programming?
A striking pathology of semidefinite programs (SDPs) is illustrated by a classical example of Khachiyan: feasible solutions in SDPs may need exponential space even to write down. Such exponential size solutions are the main obstacle to solve a long standing, fundamental open problem: can we decide feasibility of SDPs in polynomial time? The consensus seems that SDPs with large size solutions are rare. However, here we prove that they are actually quite common: a linear change of variables transforms every strictly feasible SDP into a Khachiyan type SDP, in which the leading variables are large. As to 'how large", that depends on the singularity degree of a dual problem. Further, we present some SDPs in which large solutions appear naturally, without any change of variables. We also partially answer the question: how do we represent such large solutions in polynomial space?
Joint work with Alex Touzov
Zoom Participation. See announcement.
Event Website:
https://www.cmu.edu/math/news-events/calendar.html#event=76103642;instance=20230406143000?popup=1