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SUMMARY:Accelerated Inertial Gradient Algorithms with Vanishing Tikhonov R
 egularization
DTSTART:20260424T090000Z
DTEND:20260424T093000Z
DTSTAMP:20260606T070500Z
UID:indico-event-16757@indico.math.cnrs.fr
DESCRIPTION:Speakers: Huu Nhan Nguyen\n\nWe study a first-order gradient a
 lgorithm to find the minimum-norm solution of a smooth convex minimizatio
 n problem with Lipschitz continuous gradient. The algorithm is derived vi
 a an explicit time discretization of a damped inertial system with vanishi
 ng Tikhonov regularization. For general Tikhonov regularization parameter
 s\, we establish a Lyapunov-type analysis under appropriate control of th
 e decay rate of the Tikhonov term. For polynomial choice of Tikhonov terms
  $\\varepsilon_k = k^{−p}$ with $0 < p < 2$\, we provide a fast converge
 nce rate for the objective values and prove the strong convergence of the 
 iterates to the minimum-norm minimizer. In the critical case $p = 2$\, our
  analysis ensures the fast convergence of the objective values\, but it do
 es not guarantee the strong convergence to the minimum-norm minimizer.\n\n
 https://indico.math.cnrs.fr/event/16757/
LOCATION:XR203 (XLIM)
URL:https://indico.math.cnrs.fr/event/16757/
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