Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Distributed Newton Approach for Joint Multi-Hop Routing and Flow
  Control: Theory and Algorithm   The fast growing scale and heterogeneity of current communication networks
necessitate the design of distributed cross-layer optimization algorithms. So
far, the standard approach of distributed cross-layer design is based on dual
decomposition and the subgradient algorithm, which is a first-order method that
has a slow convergence rate. In this paper, we focus on solving a joint
multi-path routing and flow control (MRFC) problem by designing a new
distributed Newton's method, which is a second-order method and enjoys a
quadratic rate of convergence. The major challenges in developing a distributed
Newton's method lie in decentralizing the computation of the Hessian matrix and
its inverse for both the primal Newton direction and dual variable updates. By
appropriately reformulating, rearranging, and exploiting the special problem
structures, we show that it is possible to decompose such computations into
source nodes and links in the network, thus eliminating the need for global
information. Furthermore, we derive closed-form expressions for both the primal
Newton direction and dual variable updates, thus significantly reducing the
computational complexity. The most attractive feature of our proposed
distributed Newton's method is that it requires almost the same scale of
information exchange as in first-order methods, while achieving a quadratic
rate of convergence as in centralized Newton methods. We provide extensive
numerical results to demonstrate the efficacy of our proposed algorithm. Our
work contributes to the advanced paradigm shift in cross-layer network design
that is evolving from first-order to second-order methods.

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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc