Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distributive Network Utility Maximization (NUM) over Time-Varying Fading
  Channels   Distributed network utility maximization (NUM) has received an increasing
intensity of interest over the past few years. Distributed solutions (e.g., the
primal-dual gradient method) have been intensively investigated under fading
channels. As such distributed solutions involve iterative updating and explicit
message passing, it is unrealistic to assume that the wireless channel remains
unchanged during the iterations. Unfortunately, the behavior of those
distributed solutions under time-varying channels is in general unknown. In
this paper, we shall investigate the convergence behavior and tracking errors
of the iterative primal-dual scaled gradient algorithm (PDSGA) with dynamic
scaling matrices (DSC) for solving distributive NUM problems under time-varying
fading channels. We shall also study a specific application example, namely the
multi-commodity flow control and multi-carrier power allocation problem in
multi-hop ad hoc networks. Our analysis shows that the PDSGA converges to a
limit region rather than a single point under the finite state Markov chain
(FSMC) fading channels. We also show that the order of growth of the tracking
errors is given by O(T/N), where T and N are the update interval and the
average sojourn time of the FSMC, respectively. Based on this analysis, we
derive a low complexity distributive adaptation algorithm for determining the
adaptive scaling matrices, which can be implemented distributively at each
transmitter. The numerical results show the superior performance of the
proposed dynamic scaling matrix algorithm over several baseline schemes, such
as the regular primal-dual gradient algorithm.

34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
19
The categories of this paper are: eess