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DTSTAMP:20240722T065544Z
SUMMARY:Andersen Ang (University of Southampton): MGProx: A nonsmooth multi
grid proximal gradient method with adaptive restriction for strongly conve
x optimization
DESCRIPTION:\nTitle\nMGProx: A nonsmooth multigrid proximal gradient method
with adaptive restriction for strongly convex optimization\n\n\nAbstract\
n\n\nWe study the combination of proximal gradient descent with multigrid
for solving a class of possibly nonsmooth convex optimization problems. We
propose a multigrid proximal gradient method called MGProx\, which accele
rates the proximal gradient method by multigrid\, based on utilizing hiera
rchical information of the optimization problem. MGProx applies a newly in
troduced adaptive restriction operator to simplify the Minkowski sum of su
bdifferentials of the nondifferentiable objective function across differen
t levels. We provide a theoretical characterization of MGProx. First we sh
ow that variables at all levels exhibit a fixed-point property at converge
nce. Next\, we show that the coarse correction is a descent direction for
the fine variable in the general nonsmooth case. Lastly\, under some mild
assumptions we provide the O(1/k2) convergence rate for the algorithm. In
the numerical experiments\, we show that MGProx has a significantly faster
convergence speed than proximal gradient descent and proximal gradient de
scent with Nesterovâ€™s acceleration on nonsmooth convex optimization prob
lems such as the Elastic Obstacle Problem. If time permits we will talk ab
out the extension to primal-dual algorithm\, ADMM and also to non-convex n
on-proximable problems.\n\n\nJoint work with Hans De Sterck (U. Waterloo)
and Stephen Vavasis (U. Waterloo)\, arXiv 2302.04077\n\n\n\nBio\n\n\nAnder
sen Ang is a lecturer (UK system\, equivalent to assistant professor in US
) in the ECS at the University of Southampton\, UK. Previously\, he is a F
ields postdoctoral fellow in the Department of Combinatorics and Optimizat
ion at the University of Waterloo\, Canada\, where his advisors are Stephe
n Vavasis and Hans De Sterck. He completed his PhD in applied mathematics
in October 2020\, associated with the Department of mathematics and operat
ions research at the University of Mons\, Belgium. His PhD supervisor is N
icolas Gillis. He received a BEng degree\, in Electronic and Communication
Engineering\, in 2014\, and a MPhil degree\, in Biomedical Engineering in
2016\, all from the University of Hong Kong\, Hong Kong. His research int
erests are general topics on the theory and application of optimization an
d matrix-tensor factorizations in machine learning.\n\n
URL:https://www.imperial.ac.uk/events/166691/andersen-ang-university-of-sou
thampton-mgprox-a-nonsmooth-multigrid-proximal-gradient-method-with-adapti
ve-restriction-for-strongly-convex-optimization/
DTSTART;TZID=Europe/London:20231011T140000
DTEND;TZID=Europe/London:20231011T150000
LOCATION:408\, Huxley Building\, South Kensington Campus\, Imperial College
London\, London\, SW7 2AZ\, United Kingdom
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