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SUMMARY:Coralia Carțiș (University of Oxford)
DTSTART:20200727T130000Z
DTEND:20200727T140000Z
DTSTAMP:20260423T021057Z
UID:OWOS/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWOS/15/">Te
 nsor Methods for Non-convex Optimization Problems</a>\nby Coralia Carțiș
  (University of Oxford) as part of One World Optimization seminar\n\n\nAbs
 tract\nWe investigate the evaluation complexity of finding high-order crit
 ical points of non-convex smooth optimization problems when high order der
 ivatives of the objective are available.\nAdaptive regularisation (and tim
 e permitting trust region) methods are presented that use high-degree Tayl
 or local models in a simple framework. Their global rates of convergence t
 o\nstandard notions of first\, second and third order critical points of t
 he objective are presented\, and observed to be natural generalisations of
  the optimal bounds known for cubic regularisation.\nHowever\, going beyon
 d third-order criticality is challenging\, requiring new notions of (appro
 ximate) high-order optimality. A strong\, stable notion of a high-order lo
 cal minimizer is presented\,\nalong with associated regularisation and tru
 st-region variants that can find such points in a quantifiable way from a 
 complexity viewpoint. Extensions of these methods and results to composite
 \noptimization\, as well as to special structure functions (such as those 
 satisfying the PL inequality) may also be discussed\, time permitting. Thi
 s work is joint with Nick Gould (Rutherford Appleton\nLaboratory\, UK) and
  Philippe Toint (University of Namur\, Belgium).\n\nthe address and passwo
 rd of the zoom room of the seminar are sent by e-mail on the mailinglist o
 f the seminar one day before each talk\n
LOCATION:https://researchseminars.org/talk/OWOS/15/
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