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CATEGORIES:CUED Control Group Seminars
SUMMARY:Saddle-point dynamics\, non-expansive semiflows\,
and necessary and sufficient conditions for conver
gence - Dr Ioannis Lestas (University of Cambridge
)
DTSTART;TZID=Europe/London:20220217T140000
DTEND;TZID=Europe/London:20220217T150000
UID:TALK170444AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/170444
DESCRIPTION:Finding the saddle point of a concave-convex funct
ion is a problem that has been widely studied in s
ince the 1950s in diverse areas and forms the basi
s of many classes of distributed optimisation algo
rithms. Nevertheless\, in broad classes of problem
s there are features that render the analysis of t
he asymptotic behaviour of saddle-point dynamics n
ontrivial. In particular\, even though for a stric
tly concave-convex function convergence to a saddl
e-point via gradient dynamics is ensured\, when th
is strictness is lacking\, convergence is not guar
anteed and oscillatory solutions can occur. Furthe
rmore\, when the subgradient method is used to res
trict the dynamics in a convex domain\, the dynami
cs become non-smooth in continuous time\, thus inc
reasing significantly the complexity in the analys
is.\n\nIn this talk we provide an explicit charact
erization to the asymptotic behaviour of gradient
dynamics for saddle-point problems. In particular\
, we show that despite the nonlinear and non-smoot
h character of these dynamics their omega-limit se
t is comprised of trajectories that solve only lin
ear ODEs that can be explicitly characterized. The
se results are used to formulate corresponding con
vergence criteria and various examples will also b
e discussed.\n
LOCATION:Dyson Seminar Room\, Department of Engineering / O
nline (Zoom)
CONTACT:Xiaodong Cheng
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