Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Distributed Optimization over Directed Networks   In this paper, we propose a distributed algorithm, called
Directed-Distributed Gradient Descent (D-DGD), to solve multi-agent
optimization problems over directed graphs. Existing algorithms mostly deal
with similar problems under the assumption of undirected networks, i.e.,
requiring the weight matrices to be doubly-stochastic. The row-stochasticity of
the weight matrix guarantees that all agents reach consensus, while the
column-stochasticity ensures that each agent's local gradient contributes
equally to the global objective. In a directed graph, however, it may not be
possible to construct a doubly-stochastic weight matrix in a distributed
manner. We overcome this difficulty by augmenting an additional variable for
each agent to record the change in the state evolution. In each iteration, the
algorithm simultaneously constructs a row-stochastic matrix and a
column-stochastic matrix instead of only a doubly-stochastic matrix. The
convergence of the new weight matrix, depending on the row-stochastic and
column-stochastic matrices, ensures agents to reach both consensus and
optimality. The analysis shows that the proposed algorithm converges at a rate
of $O(\frac{\ln k}{\sqrt{k}})$, where $k$ is the number of iterations.

24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org