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UID:20260616T224304EDT-4592Am59O5@132.216.98.100
DTSTAMP:20260617T024304Z
DESCRIPTION:Title:Storage optimal semidefinite programming\n\nAbstract: Sem
 idefinite convex optimization problems often have low-rank solutions that 
 can be represented with O(p)-storage. However\, semidefinite programming m
 ethods require us to store the matrix decision variable with size O(p^2)\,
  which prevents the application of virtually all convex methods at large s
 cale. Indeed\, storage\, not arithmetic computation\, is now the obstacle 
 that prevents us from solving large- scale optimization problems. A grand 
 challenge in contemporary optimization is therefore to design storage-opti
 mal algorithms that provably and reliably solve large-scale optimization p
 roblems in key scientific and engineering applications. An algorithm is ca
 lled storage optimal if its working storage is within a constant factor of
  the memory required to specify a generic problem instance and its solutio
 n.\n	So far\, convex methods have completely failed to satisfy storage opti
 mality. As a result\, the literature has largely focused on storage optima
 l non-convex methods to obtain numerical solutions. Unfortunately\, these 
 algorithms have been shown to be provably correct only under unverifiable 
 and unrealistic statistical assumptions on the problem template. They can 
 also sacrifice the key benefits of convexity\, as they do not use key conv
 ex geometric properties in their cost functions.  To this end\, my talk in
 troduces a new convex optimization algebra to obtain numerical solutions t
 o semidefinite programs with a low-rank matrix streaming model. This strea
 ming model provides us an opportunity to integrate sketching as a new tool
  for developing storage optimal convex optimization methods that go beyond
  semidefinite programming to more general convex templates. The resulting 
 algorithms are expected to achieve unparalleled results for scalable matri
 x optimization problems in signal processing\, machine learning\, and comp
 uter science.\n
DTSTART:20181203T210000Z
DTEND:20181203T220000Z
LOCATION:Room 1104\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Volkan Cevher (École Polytechnique Fédérale de Lausanne)
URL:/mathstat/channels/event/volkan-cevher-ecole-polyt
 echnique-federale-de-lausanne-292100
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