Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Push-Pull Gradient Method for Distributed Optimization in Networks   In this paper, we focus on solving a distributed convex optimization problem
in a network, where each agent has its own convex cost function and the goal is
to minimize the sum of the agents' cost functions while obeying the network
connectivity structure. In order to minimize the sum of the cost functions, we
consider a new distributed gradient-based method where each node maintains two
estimates, namely, an estimate of the optimal decision variable and an estimate
of the gradient for the average of the agents' objective functions. From the
viewpoint of an agent, the information about the decision variable is pushed to
the neighbors, while the information about the gradients is pulled from the
neighbors (hence giving the name "push-pull gradient method"). The method
unifies the algorithms with different types of distributed architecture,
including decentralized (peer-to-peer), centralized (master-slave), and
semi-centralized (leader-follower) architecture. We show that the algorithm
converges linearly for strongly convex and smooth objective functions over a
directed static network. In our numerical test, the algorithm performs well
even for time-varying directed networks.

28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
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