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CATEGORIES:Cambridge Image Analysis Seminars
SUMMARY:Generalized Conditional Gradient with Augmented La
grangian for Composite Minimization - Exact and In
exact Perspectives - Antonio Silveti Falls\, ENSIC
AEN France
DTSTART;TZID=Europe/London:20191009T160000
DTEND;TZID=Europe/London:20191009T170000
UID:TALK131173AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/131173
DESCRIPTION:We propose a splitting scheme which hybridizes gen
eralized conditional gradient with a proximal step
\, which we call CGALP algorithm\, for minimizing
the sum of three proper convex and lower-semiconti
nuous functions in real Hilbert spaces. The minimi
zation is subject to an affine constraint\, that a
llows in particular to deal with composite problem
s (sum of more than three functions) in a separate
way by the usual product space technique. While c
lassical conditional gradient methods require Lips
chitz-continuity of the gradient of the differenti
able part of the objective\, CGALP needs only diff
erentiability (on an appropriate subset)\, hence c
ircumventing the intricate question of Lipschitz c
ontinuity of gradients. For the two remaining func
tions in the objective\, we do not require any add
itional regularity assumption. The second function
\, possibly nonsmooth\, is assumed simple\, i.e.\,
the associated proximal mapping is easily computa
ble. For the third function\, again nonsmooth\, we
just assume that its domain is weakly compact and
that a linearly perturbed minimization oracle is
accessible. Finally\, the affine constraint is add
ressed by the augmented Lagrangian approach. We di
scuss both exact and inexact (stochastic) variants
of the algorithm.
LOCATION:MR21\, Centre for Mathematical Sciences
CONTACT:Jingwei Liang
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