Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fast convex optimization via inertial dynamics combining viscous and
  Hessian-driven damping with time rescaling   In a Hilbert setting, we develop fast methods for convex unconstrained
optimization. We rely on the asymptotic behavior of an inertial system
combining geometric damping with temporal scaling. The convex function to
minimize enters the dynamic via its gradient. The dynamic includes three
coefficients varying with time, one is a viscous damping coefficient, the
second is attached to the Hessian-driven damping, the third is a time scaling
coefficient. We study the convergence rate of the values under general
conditions involving the damping and the time scale coefficients. The obtained
results are based on a new Lyapunov analysis and they encompass known results
on the subject. We pay particular attention to the case of an asymptotically
vanishing viscous damping, which is directly related to the accelerated
gradient method of Nesterov. The Hessian-driven damping significantly reduces
the oscillatory aspects. As a main result, we obtain an exponential rate of
convergence of values without assuming the strong convexity of the objective
function. The temporal discretization of these dynamics opens the gate to a
large class of inertial optimization algorithms.

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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph