Spectrahedral shadows
classification
🧮 math.OC
math.AG
keywords
answercompactconjectureconvexeuclideanfalsegiveshelton-nie
read the original abstract
We show that there are many (compact) convex semi-algebraic sets in euclidean space that do not have a semidefinite representation. This gives a negative answer to a question by Nemirovski, resp. it shows that the Helton-Nie conjecture is false.
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