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UID:20250810T060430EDT-6806VnkBxV@132.216.98.100
DTSTAMP:20250810T100430Z
DESCRIPTION:Title: Well-posedness and Stability of Nuclear Norm Minimizatio
 n Problems\n\nAbstract :\n\nA nuclear norm minimization (NNM) problem mini
 mizing a nuclear norm over an affine constraint has many applications in r
 ecommendation systems\, computer vision\, and multivariate linear regressi
 on. It is especially efficient in recovering a low-rank matrix with known 
 linear sampling measurements. The theory of such recovery usually requires
  well-posedness and robustness on the corresponding NNM problem\, which ar
 e very likely when the number of sampling measurements is big enough. In t
 his talk\, I will provide new results in this direction. Particularly\, ge
 ometric characterizations of well-posedness are obtained via the radial/ta
 ngent cones and numerically verified. This allows us to derive the smalles
 t bound for the number of sampling measurements in exact recovery. Unique 
 solutions of NNM problems are categorized into two groups: sharp minimizer
 s and strong minimizers. When the number of measurements is not big enough
 \, unique solutions of NNM problems happen to be strong minimizers. Robust
  recovery and Lipschitz stability of NNM problems are also studied when th
 e sampling measurements are disrupted by small noises.\n
DTSTART:20240122T210000Z
DTEND:20240122T220000Z
LOCATION:Room 1104\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Nghia T. A. Tran (Oakland University)
URL:/mathstat/channels/event/nghia-t-tran-oakland-univ
 ersity-354202
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