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SUMMARY:The A-Truncated K-Moment Problem - Nie\, J (University of Californ
 ia\, San Diego)
DTSTART:20130718T133000Z
DTEND:20130718T140000Z
UID:TALK46281@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Let A be a finite subset of N^n\, and K be a compact semialgeb
 raic set. An A-tms is a vector y indexed by elements in A. The A-Truncated
  K-Moment Problem (A-TKMP) studies whether a given A-tms y admits a K-meas
 ure\n\n(i.e.\, a Borel measure supported in K) or not. We propose a numeri
 cal algorithm for solving A-TKMPs. It is based on finding a flat extension
  of y by solving a hierarchy of semidefinite relaxations\, whose objective
  R is generated in a certain randomized way. If y admits no K-measures and
  R[x]_A is K-full\, we can get a certificate for the nonexistence of repre
 senting measures. If y admits a K-measure\, then for almost all generated 
 R\, we prove\n\nthat: i) we can asymptotically get a flat extension of y\;
  ii) under a general condition that is almost sufficient and necessary\, w
 e can get a flat\n\nextension of y. The complete positive matrix decomposi
 tion and sum of even powers of linear forms decomposition problems can be 
 solved as an A-TKMP.\n\n
LOCATION:Seminar Room 1\, Newton Institute
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