BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Saddle-point dynamics\, non-expansive semiflows\, and necessary an
 d sufficient conditions for convergence - Dr Ioannis Lestas (University of
  Cambridge)
DTSTART:20220217T140000Z
DTEND:20220217T150000Z
UID:TALK170444@talks.cam.ac.uk
CONTACT:Xiaodong Cheng
DESCRIPTION:Finding the saddle point of a concave-convex function is a pro
 blem that has been widely studied in since the 1950s in diverse areas and 
 forms the basis of many classes of distributed optimisation algorithms. Ne
 vertheless\, in broad classes of problems there are features that render t
 he analysis of the asymptotic behaviour of saddle-point dynamics nontrivia
 l. In particular\, even though for a strictly concave-convex function conv
 ergence to a saddle-point via gradient dynamics is ensured\, when this str
 ictness is lacking\, convergence is not guaranteed and oscillatory solutio
 ns can occur. Furthermore\, when the subgradient method is used to restric
 t the dynamics in a convex domain\, the dynamics become non-smooth in cont
 inuous time\, thus increasing significantly the complexity in the analysis
 .\n\nIn this talk we provide an explicit characterization to the asymptoti
 c behaviour of gradient dynamics for saddle-point problems. In particular\
 , we show that despite the nonlinear and non-smooth character of these dyn
 amics their omega-limit set is comprised of trajectories that solve only l
 inear ODEs that can be explicitly characterized. These results are used to
  formulate corresponding convergence criteria and various examples will al
 so be discussed.\n
LOCATION:Dyson Seminar Room\, Department of Engineering / Online (Zoom)
END:VEVENT
END:VCALENDAR