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DTSTART:20260329T030000
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DTSTAMP:20260529T173403Z
UID:1779458400@ist.ac.at
DTSTART:20260522T160000
DTEND:20260522T170000
DESCRIPTION:Speaker: Jeferson Zapata\nhosted by Matthew Kwan\nAbstract: Sta
 ndard mathematical optimization and root-finding algorithms often stall or
  fail when faced with degenerate or singular problems. This thesis present
 s novel symbolic-numeric frameworks designed to overcome these theoretical
  and computational bottlenecks. The first part of the presentation introdu
 ces a hybrid algorithm that reformulates weakly feasible\, degenerate semi
 definite programs (SDPs) into structured polynomial systems\, enabling the
  rigorous algebraic certification of numerical approximations. The second 
 part addresses the loss of convergence in path-tracking methods near isola
 ted singular roots. By modeling solution paths as generalized fractional P
 uiseux series and utilizing an explicitly derived algebraic predictor\, th
 e proposed algorithms restore superlinear convergence and significantly re
 duce computational overhead in heavily degenerate systems.
LOCATION:Office Bldg West / Ground floor / Heinzel Seminar Room (I21.EG.101
 ) and Zoom\, ISTA
ORGANIZER:
SUMMARY:Jeferson Zapata: Thesis Defense: Overcoming Degeneracy and Singular
 ity: Techniques for Semidefinite Programs and Homotopy Continuation Endgam
 es
URL:https://talks-calendar.ista.ac.at/events/6476
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