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- W2592347948 abstract "We consider the dynamical system $$displaystyle begin {cases} v(t)in partial phi (x(t)) lambda dot x(t) + dot v(t) + v(t) + nabla psi (x(t))=0, end {cases} $$where (phi :mathbb {R}^nto mathbb {R}cup {+infty }) is a proper, convex, and lower semicontinuous function, (psi :mathbb {R}^nto mathbb {R}) is a (possibly nonconvex) smooth function, and λ > 0 is a parameter which controls the velocity. We show that the set of limit points of the trajectory x is contained in the set of critical points of the objective function ϕ + ψ, which is here seen as the set of the zeros of its limiting subdifferential. If the objective function is smooth and satisfies the Kurdyka-Łojasiewicz property, then we can prove convergence of the whole trajectory x to a critical point. Furthermore, convergence rates for the orbits are obtained in terms of the Łojasiewicz exponent of the objective function, provided the latter satisfies the Łojasiewicz property." @default.
- W2592347948 created "2017-03-16" @default.
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- W2592347948 date "2019-01-01" @default.
- W2592347948 modified "2023-10-17" @default.
- W2592347948 title "Newton-Like Dynamics Associated to Nonconvex Optimization Problems" @default.
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- W2592347948 doi "https://doi.org/10.1007/978-3-030-11370-4_6" @default.
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