Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Accelerated Optimization on Riemannian Manifolds via Projected
  Variational Integrators   A variational formulation of accelerated optimization on normed spaces was
recently introduced by considering a specific family of time-dependent Bregman
Lagrangian and Hamiltonian systems whose corresponding trajectories converge to
the minimizer of the given convex function at an arbitrary accelerated rate of
$\mathcal{O}(1/t^p)$. This framework has been exploited using time-adaptive
geometric integrators to design efficient explicit algorithms for symplectic
accelerated optimization. It was observed that geometric discretizations were
substantially less prone to stability issues, and were therefore more robust,
reliable, and computationally efficient. More recently, this variational
framework has been extended to the Riemannian manifold setting by considering a
more general family of time-dependent Bregman Lagrangian and Hamiltonian
systems on Riemannian manifolds. It is thus natural to develop time-adaptive
Hamiltonian variational integrators for accelerated optimization on Riemannian
manifolds. In the past, Hamiltonian variational integrators have been
constructed with holonomic constraints, but the resulting algorithms were
implicit in nature, which significantly increased their cost per iteration. In
this paper, we will test the performance of explicit methods based on
Hamiltonian variational integrators combined with projections that constrain
the numerical solution to remain on the constraint manifold.

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The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys