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PRODID:-//talks.bham.ac.uk//v3//EN
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CATEGORIES:Optimisation and Numerical Analysis Seminars
SUMMARY:On the Existence of Affine Invariant Descent Direc
tions - Florian Jarre (Heinrich-Heine-Universit\\&
quot\;at D\\"\;usseldorf)
DTSTART:20181011T110000Z
DTEND:20181011T120000Z
UID:TALK3296AT
URL:/talk/index/3296
DESCRIPTION:A prominent example of a polynomial time algorithm
ic scheme are interior-point methods for convex op
timization.\nIn this setting\, affine invariance i
s crucial for the analysis. In this talk the exist
ence of affine invariant descent directions for un
constrained minimization is discussed. While there
may exist several affine invariant descent direct
ions for smooth functions at a given point\, there
exists exactly one in the case of strictly convex
quadratic functions and generally none in the cas
e of quadratic functions with singular or indefini
te Hessian.\nThese results can be generalized to s
mooth nonlinear functions and have implications re
garding the initialization of minimization algorit
hms. They stand in contrast to recent works on con
strained convex and nonconvex optimization for whi
ch there may exist an affine invariant ``frame'' t
hat depends on the feasible set and that can be us
ed to define an affine invariant descent direction
.\n\nJoint work with Yu-Hong Dai and Felix Lieder.
\n
LOCATION:Nuffield G13
CONTACT:Sergey Sergeev
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