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Article overview
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Asymptotic for the perturbed heavy ball system with vanishing damping term | Mounir Balti
; Ramzi May
; | Date: |
1 Sep 2016 | Abstract: | We investigate the long time behavior of solutions to the differential
equation $ddot{x}(t)+frac{c}{left( t+1
ight) ^{alpha}}dot{x}(t)+
abla
Phileft( x(t)
ight) =g(t),~tgeq0, $ where $c$ is nonnegative constant,
$alphainlbrack0,1[,$ $Phi$ is a $C^{1}$ convex function on a Hilbert space
$mathcal{H}$ and $gin L^{1} (0,+infty;mathcal{H}).$ We obtain sufficient
conditions on the source term $g(t)$ ensuring the weak or the strong
convergence of any trajectory $x(t)$ as $t
ightarrow+infty$ to a minimizer of
the function $Phi$ if one exists. | Source: | arXiv, 1609.0135 | Services: | Forum | Review | PDF | Favorites |
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