9,209 research outputs found
Distributed Random Convex Programming via Constraints Consensus
This paper discusses distributed approaches for the solution of random convex
programs (RCP). RCPs are convex optimization problems with a (usually large)
number N of randomly extracted constraints; they arise in several applicative
areas, especially in the context of decision under uncertainty, see [2],[3]. We
here consider a setup in which instances of the random constraints (the
scenario) are not held by a single centralized processing unit, but are
distributed among different nodes of a network. Each node "sees" only a small
subset of the constraints, and may communicate with neighbors. The objective is
to make all nodes converge to the same solution as the centralized RCP problem.
To this end, we develop two distributed algorithms that are variants of the
constraints consensus algorithm [4],[5]: the active constraints consensus (ACC)
algorithm, and the vertex constraints consensus (VCC) algorithm. We show that
the ACC algorithm computes the overall optimal solution in finite time, and
with almost surely bounded communication at each iteration. The VCC algorithm
is instead tailored for the special case in which the constraint functions are
convex also w.r.t. the uncertain parameters, and it computes the solution in a
number of iterations bounded by the diameter of the communication graph. We
further devise a variant of the VCC algorithm, namely quantized vertex
constraints consensus (qVCC), to cope with the case in which communication
bandwidth among processors is bounded. We discuss several applications of the
proposed distributed techniques, including estimation, classification, and
random model predictive control, and we present a numerical analysis of the
performance of the proposed methods. As a complementary numerical result, we
show that the parallel computation of the scenario solution using ACC algorithm
significantly outperforms its centralized equivalent
Randomized Constraints Consensus for Distributed Robust Linear Programming
In this paper we consider a network of processors aiming at cooperatively
solving linear programming problems subject to uncertainty. Each node only
knows a common cost function and its local uncertain constraint set. We propose
a randomized, distributed algorithm working under time-varying, asynchronous
and directed communication topology. The algorithm is based on a local
computation and communication paradigm. At each communication round, nodes
perform two updates: (i) a verification in which they check-in a randomized
setup-the robust feasibility (and hence optimality) of the candidate optimal
point, and (ii) an optimization step in which they exchange their candidate
bases (minimal sets of active constraints) with neighbors and locally solve an
optimization problem whose constraint set includes: a sampled constraint
violating the candidate optimal point (if it exists), agent's current basis and
the collection of neighbor's basis. As main result, we show that if a processor
successfully performs the verification step for a sufficient number of
communication rounds, it can stop the algorithm since a consensus has been
reached. The common solution is-with high confidence-feasible (and hence
optimal) for the entire set of uncertainty except a subset having arbitrary
small probability measure. We show the effectiveness of the proposed
distributed algorithm on a multi-core platform in which the nodes communicate
asynchronously.Comment: Accepted for publication in the 20th World Congress of the
International Federation of Automatic Control (IFAC
Distributed Partitioned Big-Data Optimization via Asynchronous Dual Decomposition
In this paper we consider a novel partitioned framework for distributed
optimization in peer-to-peer networks. In several important applications the
agents of a network have to solve an optimization problem with two key
features: (i) the dimension of the decision variable depends on the network
size, and (ii) cost function and constraints have a sparsity structure related
to the communication graph. For this class of problems a straightforward
application of existing consensus methods would show two inefficiencies: poor
scalability and redundancy of shared information. We propose an asynchronous
distributed algorithm, based on dual decomposition and coordinate methods, to
solve partitioned optimization problems. We show that, by exploiting the
problem structure, the solution can be partitioned among the nodes, so that
each node just stores a local copy of a portion of the decision variable
(rather than a copy of the entire decision vector) and solves a small-scale
local problem
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