8,571 research outputs found
A Finite-Time Cutting Plane Algorithm for Distributed Mixed Integer Linear Programming
Many problems of interest for cyber-physical network systems can be
formulated as Mixed Integer Linear Programs in which the constraints are
distributed among the agents. In this paper we propose a distributed algorithm
to solve this class of optimization problems in a peer-to-peer network with no
coordinator and with limited computation and communication capabilities. In the
proposed algorithm, at each communication round, agents solve locally a small
LP, generate suitable cutting planes, namely intersection cuts and cost-based
cuts, and communicate a fixed number of active constraints, i.e., a candidate
optimal basis. We prove that, if the cost is integer, the algorithm converges
to the lexicographically minimal optimal solution in a finite number of
communication rounds. Finally, through numerical computations, we analyze the
algorithm convergence as a function of the network size.Comment: 6 pages, 3 figure
Primal Recovery from Consensus-Based Dual Decomposition for Distributed Convex Optimization
Dual decomposition has been successfully employed in a variety of distributed
convex optimization problems solved by a network of computing and communicating
nodes. Often, when the cost function is separable but the constraints are
coupled, the dual decomposition scheme involves local parallel subgradient
calculations and a global subgradient update performed by a master node. In
this paper, we propose a consensus-based dual decomposition to remove the need
for such a master node and still enable the computing nodes to generate an
approximate dual solution for the underlying convex optimization problem. In
addition, we provide a primal recovery mechanism to allow the nodes to have
access to approximate near-optimal primal solutions. Our scheme is based on a
constant stepsize choice and the dual and primal objective convergence are
achieved up to a bounded error floor dependent on the stepsize and on the
number of consensus steps among the nodes
A Distributed Newton Method for Network Utility Maximization
Most existing work uses dual decomposition and subgradient methods to solve
Network Utility Maximization (NUM) problems in a distributed manner, which
suffer from slow rate of convergence properties. This work develops an
alternative distributed Newton-type fast converging algorithm for solving
network utility maximization problems with self-concordant utility functions.
By using novel matrix splitting techniques, both primal and dual updates for
the Newton step can be computed using iterative schemes in a decentralized
manner with limited information exchange. Similarly, the stepsize can be
obtained via an iterative consensus-based averaging scheme. We show that even
when the Newton direction and the stepsize in our method are computed within
some error (due to finite truncation of the iterative schemes), the resulting
objective function value still converges superlinearly to an explicitly
characterized error neighborhood. Simulation results demonstrate significant
convergence rate improvement of our algorithm relative to the existing
subgradient methods based on dual decomposition.Comment: 27 pages, 4 figures, LIDS report, submitted to CDC 201
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