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Title:
Non-commutative optimization - geodesic 1st and 2nd order methods for moment maps and polytopes
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Abstract:
Scaling problems, such as operator scaling and tensor scaling, have recently found several applications in diverse areas of math and CS. They have been used to give efficient algorithms for non-commutative rational identity testing, compute the optimal constant in Brascamp-Lieb inequalities, one-body quantum marginal problem, solution to the Paulsen problem, and the search version of the Horn’s problem, to name a few, [GGOW15, GGOW18, BFGOWW18, KLLR18, F18].
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