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Distributed Lagrangian Methods for Network Resource Allocation
Motivated by a variety of applications in control engineering and information
sciences, we study network resource allocation problems where the goal is to
optimally allocate a fixed amount of resource over a network of nodes. In these
problems, due to the large scale of the network and complicated
inter-connections between nodes, any solution must be implemented in parallel
and based only on local data resulting in a need for distributed algorithms. In
this paper, we propose a novel distributed Lagrangian method, which requires
only local computation and communication. Our focus is to understand the
performance of this algorithm on the underlying network topology. Specifically,
we obtain an upper bound on the rate of convergence of the algorithm as a
function of the size and the topology of the underlying network. The
effectiveness and applicability of the proposed method is demonstrated by its
use in solving the important economic dispatch problem in power systems,
specifically on the benchmark IEEE-14 and IEEE-118 bus systems
On the convergence rate of distributed gradient methods for finite-sum optimization under communication delays
Motivated by applications in machine learning and statistics, we study
distributed optimization problems over a network of processors, where the goal
is to optimize a global objective composed of a sum of local functions. In
these problems, due to the large scale of the data sets, the data and
computation must be distributed over processors resulting in the need for
distributed algorithms. In this paper, we consider a popular distributed
gradient-based consensus algorithm, which only requires local computation and
communication. An important problem in this area is to analyze the convergence
rate of such algorithms in the presence of communication delays that are
inevitable in distributed systems. We prove the convergence of the
gradient-based consensus algorithm in the presence of uniform, but possibly
arbitrarily large, communication delays between the processors. Moreover, we
obtain an upper bound on the rate of convergence of the algorithm as a function
of the network size, topology, and the inter-processor communication delays
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