Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence Rates of Gradient Methods for Convex Optimization in the
  Space of Measures   We study the convergence rate of Bregman gradient methods for convex
optimization in the space of measures on a d-dimensional manifold. Under basic
regularity assumptions, we show that the suboptimality gap at iteration k is in
O(log(k)k^{--1}) for multiplicative updates, while it is in O(k^{--q/(d+q)})
for additive updates for some q = {1, 2, 4} determined by the structure of the
objective function. Our flexible proof strategy, based on approximation
arguments, allows to painlessly cover all Bregman Proximal Gradient Methods
(PGM) and their acceleration (APGM) under various geometries such as the
hyperbolic entropy and L^p divergences. We also prove the tightness of our
analysis with matching lower bounds and confirm the theoretical results with
numerical experiments on low dimensional problems. Note that all these
optimization methods must additionally pay the computational cost of
discretization, which can be exponential in d.

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The categories of this paper are: acc-phys
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess