Optimization, Algebra, and Geometry Seminar April 6, 2023 2:30pm — 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 Add event to Google Add event to iCal
