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SUMMARY:Diego Cifuentes (remote) (Georgia Tech)
DTSTART:20221110T223000Z
DTEND:20221110T233000Z
DTSTAMP:20260513T193603Z
UID:SFUOR/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SFUOR/5/">Co
 mputing the Nearest Structured Rank Deficient Matrix</a>\nby Diego Cifuent
 es (remote) (Georgia Tech) as part of PIMS-CORDS SFU Operations Research S
 eminar\n\nLecture held in ASB 10908.\n\nAbstract\nGiven an affine space of
  matrices L and a matrix Θ ∈ L\, consider the problem of computing the 
 closest rank deficient matrix to Θ on L with respect to the Frobenius nor
 m. This is a nonconvex problem with several applications in control theory
 \, computer algebra\, and computer vision. We introduce a novel semidefini
 te programming (SDP) relaxation\, and prove that it always gives the globa
 l minimizer of the nonconvex problem in the low noise regime\, i.e.\, when
  Θ is close to be rank deficient. Our SDP is the first convex relaxation 
 for this problem with provable guarantees. We evaluate the performance of 
 our SDP relaxation in examples from system identification\, approximate GC
 D\, triangulation\, and camera resectioning. Our relaxation reliably obtai
 ns the global minimizer under non-adversarial noise\, and its noise tolera
 nce is significantly better than state of the art methods.\n
LOCATION:https://researchseminars.org/talk/SFUOR/5/
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