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Article overview
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Approaching nonsmooth nonconvex optimization problems through first order dynamical systems with hidden acceleration and Hessian driven damping terms | | Radu Ioan Bot
; Ernö Robert Csetnek
; | | Date: |
4 Oct 2016 | | Abstract: | In this paper we carry out an asymptotic analysis of the proximal-gradient
dynamical system egin{equation*}left{ egin{array}{ll} dot x(t) +x(t) =
prox_{gamma f}ig[x(t)-gamma
ablaPhi(x(t))-ax(t)-by(t)ig],\ dot
y(t)+ax(t)+by(t)=0 end{array}
ight.end{equation*} where $f$ is a proper,
convex and lower semicontinuous function, $Phi$ a possibly nonconvex smooth
function and $gamma, a$ and $b$ are positive real numbers. We show that the
generated trajectories approach the set of critical points of $f+Phi$, here
understood as zeros of its limiting subdifferential, under the premise that a
regularization of this sum function satisfies the Kurdyka-L{}ojasiewicz
property. We also establish convergence rates for the trajectories, formulated
in terms of the L{}ojasiewicz exponent of the considered regularization
function. | | Source: | arXiv, 1610.0911 | | Services: | Forum | Review | PDF | Favorites | |
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