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SUMMARY:Geodesic Convex Optimization and Its Applications to Theory
DTSTART:20180719T121500
DTEND:20180719T141500
DTSTAMP:20260407T111203Z
UID:d62c32aab8586c2ef8d03a3b7423c0520c9f357fc60edacc5214c710
CATEGORIES:Conferences - Seminars
DESCRIPTION:Ozan Yildiz\nEDIC candidacy exam\nExam president: Prof. Patric
 k Thiran\nThesis advisor: Prof. Nisheeth Vishnoi\nCo-examiner: Dr. Nicolas
  Macris\n\nAbstract\nWe consider the application of geodesically convex op
 timization techniques to the computation of the optimal constant in the Br
 ascamp-Lieb inequality. The computation of the optimal constant in the Bra
 scamp-Lieb inequality is an important theoretical problem that generalizes
  other theoretical problems such as computation of the maximum entropy dis
 tribution and computation of the capacity of an operator with applications
  in machine learning\, information theory\, and theoretical computer scien
 ce. Lieb [Lie90] proved that the optimal constant in the Brascamp-Lieb ine
 quality has a non-convex optimization characterization\, and the best-know
 n algorithm to compute the optimal constant using this characterization [G
 GdOW17] runs in polynomial time in the unary bit-complexity of the input. 
 Although Lieb's characterization is non-convex\, it is jointly geodesicall
 y convex on the direct sum of canonical Hessian manifold over positive def
 inite cones. Furthermore\, it can be formulated as a geodesically convex p
 roblem on the canonical Hessian manifold over a single positive definite c
 one. Recently a polynomial time algorithm for a related problem\, operator
  scaling\, that is also geodesically convex on the same manifold\, using g
 eodesically convex optimization techniques proposed by Allen-Zhu et al. [A
 ZGL+18]. We discuss the applicability of this algorithm and other geodesic
 ally convex optimization techniques to the computation of the optimal cons
 tant in the Brascamp-Lieb inequality.\n\nBackground papers\nEntropy\, Opti
 mization and CountingMohit Singh\, Nisheeth K. Vishnoi\nAlgorithmic and Op
 timization Aspects of Brascamp-Lieb Inequalities\, via Operator Scaling\, 
 by Ankit Garg\, et al.\nOperator Scaling via Geodesically Convex Optimizat
 ion\, Invariant Theory and Polynomial Identity Testing\, by Zeyuan Allen-Z
 hu\n 
LOCATION:BC 129 https://plan.epfl.ch/?room==BC%20129
STATUS:CONFIRMED
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