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DTSTART:20240310T070000
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DTSTART;TZID=America/Toronto:20250307T153000
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URL:/combinatorics-and-optimization/events/tutte-colloq
 uium-yuen-man-pun
SUMMARY:Tutte colloquium-Yuen-Man Pun
CLASS:PUBLIC
DESCRIPTION:Summary \n\nTITLE:Benign Optimization Landscape of Formulations
  for\nTime-of-Arrival-Based Source Localization Problem\n\nSPEAKER:\n Yuen
 -Man Pun\n\nAFFILIATION:\n Australian National University\n\nLOCATION:\n M
 C 5501\n\nABSTRACT: : In this talk\, we will address the maximum-likeliho
 od (ML)\nformulation and a least-squares (LS) formulation of the\ntime-of-
 arrival (TOA)-based source localization problem. Although both\nformulatio
 ns are generally non-convex\, we will show that they both\npossess benign 
 optimization landscape. First\, we consider the ML\nformulation of the TOA
 -based source localization problem. Under\nstandard assumptions on the TOA
  measurement model\, we will show a\nbound on the distance between an opti
 mal solution and the true target\nposition and establish the local strong 
 convexity of the ML function\nat its global minima. Second\, we consider t
 he LS formulation of the\nTOA-based source localization problem. We will s
 how that the LS\nformulation is globally strongly convex under certain con
 dition on the\ngeometric configuration of the anchors and the source and o
 n the\nmeasurement noise. We will then derive a characterization of the\nc
 ritical points of the LS formulation\, which leads to a bound on the\nmaxi
 mum number of critical points under a very mild assumption on the\nmeasure
 ment noise and a sufficient condition for the critical points\nof the LS f
 ormulation to be isolated. The said characterization also\nleads to an alg
 orithm that can find a global optimum of the LS\nformulation by searching 
 through all critical points. Lastly\, we will\ndiscuss some possible futur
 e directions.\n\n \n\n \n 
DTSTAMP:20250705T133354Z
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