Title
Approaching Nonsmooth Nonconvex Optimization Problems Through First Order Dynamical Systems with Hidden Acceleration and Hessian Driven Damping Terms
Author
Abstract
In this paper we carry out an asymptotic analysis of the proximal-gradient dynamical system
{x˙(t)+x(t)=proxγf[x(t)−γ∇Φ(x(t))−ax(t)−by(t)],y˙(t)+ax(t)+by(t)=0
where f is a proper, convex and lower semicontinuous function, Φ a possibly nonconvex smooth function and γ,a and b are positive real numbers. We show that the generated trajectories approach the set of critical points of f + Φ, here understood as zeros of its limiting subdifferential, under the premise that a regularization of this sum function satisfies the Kurdyka-Łojasiewicz property. We also establish convergence rates for the trajectories, formulated in terms of the Łojasiewicz exponent of the considered regularization function.
Keywords
Dynamical systemsLyapunov analysisNonsmooth optimizationLimiting subdifferentialKurdyka-Łojasiewicz property
Object type
Language
English [eng]
Persistent identifier
Appeared in
Title
Set-Valued and Variational Analysis
Publication
Springer Nature
Version type
Date issued
2017
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Rights
Rights statement
© The Author(s) 2017
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