Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence of Limited Communications Gradient Methods   Distributed optimization increasingly plays a central role in economical and
sustainable operation of cyber-physical systems. Nevertheless, the complete
potential of the technology has not yet been fully exploited in practice due to
communication limitations posed by the real-world infrastructures. This work
investigates fundamental properties of distributed optimization based on
gradient methods, where gradient information is communicated using limited
number of bits. In particular, a general class of quantized gradient methods
are studied where the gradient direction is approximated by a finite
quantization set. Sufficient and necessary conditions are provided on such a
quantization set to guarantee that the methods minimize any convex objective
function with Lipschitz continuous gradient and a nonempty and bounded set of
optimizers. A lower bound on the cardinality of the quantization set is
provided, along with specific examples of minimal quantizations. Convergence
rate results are established that connect the fineness of the quantization and
the number of iterations needed to reach a predefined solution accuracy.
Generalizations of the results to a relevant class of constrained problems
using projections are considered. Finally, the results are illustrated by
simulations of practical systems.

37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
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The categories of this paper are: eess
11
The categories of this paper are: hep-lat