Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distributed optimization over time-varying directed graphs   We consider distributed optimization by a collection of nodes, each having
access to its own convex function, whose collective goal is to minimize the sum
of the functions. The communications between nodes are described by a
time-varying sequence of directed graphs, which is uniformly strongly
connected. For such communications, assuming that every node knows its
out-degree, we develop a broadcast-based algorithm, termed the
subgradient-push, which steers every node to an optimal value under a standard
assumption of subgradient boundedness. The subgradient-push requires no
knowledge of either the number of agents or the graph sequence to implement.
Our analysis shows that the subgradient-push algorithm converges at a rate of
$O(\ln(t)/\sqrt{t})$, where the constant depends on the initial values at the
nodes, the subgradient norms, and, more interestingly, on both the consensus
speed and the imbalances of influence among the nodes.

10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph