Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Newton-like dynamics associated to nonconvex optimization problems   We consider the dynamical system \begin{equation*}\left\{ \begin{array}{ll}
v(t)\in\partial\phi(x(t))\\ \lambda\dot x(t) + \dot v(t) + v(t) + \nabla
\psi(x(t))=0, \end{array}\right.\end{equation*} where
$\phi:\R^n\to\R\cup\{+\infty\}$ is a proper, convex and lower semicontinuous
function, $\psi:\R^n\to\R$ is a (possibly nonconvex) smooth function and
$\lambda>0$ 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 $\phi+\psi$, which is here seen as the set of the
zeros of its limiting subdifferential. If the objective function satisfies the
Kurdyka-\L{}ojasiewicz 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 \L{}ojasiewicz exponent of the objective
function, provided the latter satisfies the \L{}ojasiewicz property.

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The categories of this paper are: physics
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph