BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:CUED Control Group Seminars
SUMMARY:Gradient systems: overview and recent results - Dr
Pierre-Antoine Absil (Department of Mathematical
Engineering\, Universite catholique de Louvain\, L
ouvain-la-Neuve\, Belgium)
DTSTART;TZID=Europe/London:20090501T140000
DTEND;TZID=Europe/London:20090501T150000
UID:TALK15000AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/15000
DESCRIPTION:A continuous-time gradient system is a dynamical s
ystem of the form dx/dt = - grad f(x)\, where grad
f denotes the gradient of the differentiable real
-valued function f\, whose domain is the Euclidean
space R^n or more generally a (smooth) manifold M
. A discrete-time gradient system takes the form x
_{k+1} = x_k - s grad f(x)\, where the step size s
can be chosen by various means.\n\nGradient syste
ms are useful in solving various optimization-rela
ted problems\, e.g.\, in principal component analy
sis\, optimal control\, balanced realizations\, oc
ean sampling\, noise reduction\, pose estimation o
r the Procrustes problem.\n\nIn this talk\, we pre
sent recent (and less recent) results pertaining t
o the convergence of the solutions of gradient sys
tems. In particular\, we are interested in reasona
bly weak conditions\, sufficient for the solution
trajectories to have at most one accumulation poin
t. \n\nIn a similar spirit\, we discuss the notion
of "accelerated" descent methods. This notion was
formalized only recently\, but the principles hav
e been in hiding in several places\, notably the w
ork of D. Bertsekas and E. Polak. The idea is as f
ollows. If T denotes a descent iteration for f\, w
e say that a sequence {x_k} is T-accelerated if th
e decrease of f between x_k and x_{k+1} is at leas
t as good as the decrease of f between x_k and T(x
_k). We address the following question: Assume tha
t all the accumulation points of every sequence {y
_k} satisfying y_{k+1} = T(y_k) are critical point
s of f\; what can be said about the accumulation p
oints of T-accelerated sequences? This question ap
pears in the analysis of several numerical algorit
hms.
LOCATION:Cambridge University Engineering Department\, Lect
ure Room 3B
CONTACT:Dr Guy-Bart Stan
END:VEVENT
END:VCALENDAR