255 research outputs found
Distributed Nonconvex Multiagent Optimization Over Time-Varying Networks
We study nonconvex distributed optimization in multiagent networks where the
communications between nodes is modeled as a time-varying sequence of arbitrary
digraphs. We introduce a novel broadcast-based distributed algorithmic
framework for the (constrained) minimization of the sum of a smooth (possibly
nonconvex and nonseparable) function, i.e., the agents' sum-utility, plus a
convex (possibly nonsmooth and nonseparable) regularizer. The latter is usually
employed to enforce some structure in the solution, typically sparsity. The
proposed method hinges on Successive Convex Approximation (SCA) techniques
coupled with i) a tracking mechanism instrumental to locally estimate the
gradients of agents' cost functions; and ii) a novel broadcast protocol to
disseminate information and distribute the computation among the agents.
Asymptotic convergence to stationary solutions is established. A key feature of
the proposed algorithm is that it neither requires the double-stochasticity of
the consensus matrices (but only column stochasticity) nor the knowledge of the
graph sequence to implement. To the best of our knowledge, the proposed
framework is the first broadcast-based distributed algorithm for convex and
nonconvex constrained optimization over arbitrary, time-varying digraphs.
Numerical results show that our algorithm outperforms current schemes on both
convex and nonconvex problems.Comment: Copyright 2001 SS&C. Published in the Proceedings of the 50th annual
Asilomar conference on signals, systems, and computers, Nov. 6-9, 2016, CA,
US
Distributed Delay-Tolerant Strategies for Equality-Constraint Sum-Preserving Resource Allocation
This paper proposes two nonlinear dynamics to solve constrained distributed
optimization problem for resource allocation over a multi-agent network. In
this setup, coupling constraint refers to resource-demand balance which is
preserved at all-times. The proposed solutions can address various model
nonlinearities, for example, due to quantization and/or saturation. Further, it
allows to reach faster convergence or to robustify the solution against
impulsive noise or uncertainties. We prove convergence over weakly connected
networks using convex analysis and Lyapunov theory. Our findings show that
convergence can be reached for general sign-preserving odd nonlinearity. We
further propose delay-tolerant mechanisms to handle general bounded
heterogeneous time-varying delays over the communication network of agents
while preserving all-time feasibility. This work finds application in CPU
scheduling and coverage control among others. This paper advances the
state-of-the-art by addressing (i) possible nonlinearity on the agents/links,
meanwhile handling (ii) resource-demand feasibility at all times, (iii)
uniform-connectivity instead of all-time connectivity, and (iv) possible
heterogeneous and time-varying delays. To our best knowledge, no existing work
addresses contributions (i)-(iv) altogether. Simulations and comparative
analysis are provided to corroborate our contributions
Distributed Primal Decomposition for Large-Scale MILPs
This paper deals with a distributed Mixed-Integer Linear Programming (MILP) set-up arising in several control applications. Agents of a network aim to minimize the sum of local linear cost functions subject to both individual constraints and a linear coupling constraint involving all the decision variables. A key, challenging feature of the considered set-up is that some components of the decision variables must assume integer values. The addressed MILPs are NP-hard, nonconvex and large-scale. Moreover, several additional challenges arise in a distributed framework due to the coupling constraint, so that feasible solutions with guaranteed suboptimality bounds are of interest. We propose a fully distributed algorithm based on a primal decomposition approach and an appropriate tightening of the coupling constraint. The algorithm is guaranteed to provide feasible solutions in finite time. Moreover, asymptotic and finite-time suboptimality bounds are established for the computed solution. Montecarlo simulations highlight the extremely low suboptimality bounds achieved by the algorithm
A Tutorial on Distributed Optimization for Cooperative Robotics: from Setups and Algorithms to Toolboxes and Research Directions
Several interesting problems in multi-robot systems can be cast in the
framework of distributed optimization. Examples include multi-robot task
allocation, vehicle routing, target protection and surveillance. While the
theoretical analysis of distributed optimization algorithms has received
significant attention, its application to cooperative robotics has not been
investigated in detail. In this paper, we show how notable scenarios in
cooperative robotics can be addressed by suitable distributed optimization
setups. Specifically, after a brief introduction on the widely investigated
consensus optimization (most suited for data analytics) and on the
partition-based setup (matching the graph structure in the optimization), we
focus on two distributed settings modeling several scenarios in cooperative
robotics, i.e., the so-called constraint-coupled and aggregative optimization
frameworks. For each one, we consider use-case applications, and we discuss
tailored distributed algorithms with their convergence properties. Then, we
revise state-of-the-art toolboxes allowing for the implementation of
distributed schemes on real networks of robots without central coordinators.
For each use case, we discuss their implementation in these toolboxes and
provide simulations and real experiments on networks of heterogeneous robots
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