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DTSTART:20240310T070000
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DTSTART:20241103T060000
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DTSTART;TZID=America/Toronto:20250307T153000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/Toronto:20250307T163000
URL:https://uwaterloo.ca/combinatorics-and-optimization/events/tutte-colloq
 uium-yuen-man-pun
SUMMARY:Tutte colloquium-Yuen-Man Pun
CLASS:PUBLIC
DESCRIPTION:TITLE:Benign Optimization Landscape of Formulations for\nTime-o
 f-Arrival-Based Source Localization Problem\n\nSPEAKER:\n Yuen-Man Pun\n\n
 AFFILIATION:\n Australian National University\n\nLOCATION:\n MC 5501\n\nAB
 STRACT: : In this talk\, we will address the maximum-likelihood (ML)\nfor
 mulation and a least-squares (LS) formulation of the\ntime-of-arrival (TOA
 )-based source localization problem. Although both\nformulations are gener
 ally non-convex\, we will show that they both\npossess benign optimization
  landscape. First\, we consider the ML\nformulation of the TOA-based sourc
 e localization problem. Under\nstandard assumptions on the TOA measurement
  model\, we will show a\nbound on the distance between an optimal solution
  and the true target\nposition and establish the local strong convexity of
  the ML function\nat its global minima. Second\, we consider the LS formul
 ation of the\nTOA-based source localization problem. We will show that the
  LS\nformulation is globally strongly convex under certain condition on th
 e\ngeometric configuration of the anchors and the source and on the\nmeasu
 rement noise. We will then derive a characterization of the\ncritical poin
 ts of the LS formulation\, which leads to a bound on the\nmaximum number o
 f critical points under a very mild assumption on the\nmeasurement noise a
 nd a sufficient condition for the critical points\nof the LS formulation t
 o be isolated. The said characterization also\nleads to an algorithm that 
 can find a global optimum of the LS\nformulation by searching through all 
 critical points. Lastly\, we will\ndiscuss some possible future directions
 .\n\n \n\n 
DTSTAMP:20260424T022852Z
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