11,548 research outputs found
Push-Pull Based Distributed Primal-Dual Algorithm for Coupled Constrained Convex Optimization in Multi-Agent Networks
This paper focuses on a distributed coupled constrained convex optimization
problem over directed unbalanced and time-varying multi-agent networks, where
the global objective function is the sum of all agents' private local objective
functions, and decisions of all agents are subject to coupled equality and
inequality constraints and a compact convex subset. In the multi-agent
networks, each agent exchanges information with other neighboring agents.
Finally, all agents reach a consensus on decisions, meanwhile achieving the
goal of minimizing the global objective function under the given constraint
conditions. For the purpose of protecting the information privacy of each
agent, we first establish the saddle point problem of the constrained convex
optimization problem considered in this article, then based on the push-pull
method, develop a distributed primal-dual algorithm to solve the dual problem.
Under Slater's condition, we will show that the sequence of points generated by
the proposed algorithm converges to a saddle point of the Lagrange function.
Moreover, we analyze the iteration complexity of the algorithm
Convergence of a Multi-Agent Projected Stochastic Gradient Algorithm for Non-Convex Optimization
We introduce a new framework for the convergence analysis of a class of
distributed constrained non-convex optimization algorithms in multi-agent
systems. The aim is to search for local minimizers of a non-convex objective
function which is supposed to be a sum of local utility functions of the
agents. The algorithm under study consists of two steps: a local stochastic
gradient descent at each agent and a gossip step that drives the network of
agents to a consensus. Under the assumption of decreasing stepsize, it is
proved that consensus is asymptotically achieved in the network and that the
algorithm converges to the set of Karush-Kuhn-Tucker points. As an important
feature, the algorithm does not require the double-stochasticity of the gossip
matrices. It is in particular suitable for use in a natural broadcast scenario
for which no feedback messages between agents are required. It is proved that
our result also holds if the number of communications in the network per unit
of time vanishes at moderate speed as time increases, allowing for potential
savings of the network's energy. Applications to power allocation in wireless
ad-hoc networks are discussed. Finally, we provide numerical results which
sustain our claims.Comment: IEEE Transactions on Automatic Control 201
Projected Push-Sum Gradient Descent-Ascent for Convex Optimizationwith Application to Economic Dispatch Problems
We propose a novel algorithm for solving convex, constrained and distributed
optimization problems defined on multi-agent-networks, where each agent has
exclusive access to a part of the global objective function. The agents are
able to exchange information over a directed, weighted communication graph,
which can be represented as a column-stochastic matrix. The algorithm combines
an adjusted push-sum consensus protocol for information diffusion and a
gradient descent-ascent on the local cost functions, providing convergence to
the optimum of their sum. We provide results on a reformulation of the push-sum
into single matrix-updates and prove convergence of the proposed algorithm to
an optimal solution, given standard assumptions in distributed optimization.
The algorithm is applied to a distributed economic dispatch problem, in which
the constraints can be expressed in local and global subsets
Distributed Big-Data Optimization via Block-Iterative Convexification and Averaging
In this paper, we study distributed big-data nonconvex optimization in
multi-agent networks. We consider the (constrained) minimization of the sum of
a smooth (possibly) nonconvex function, i.e., the agents' sum-utility, plus a
convex (possibly) nonsmooth regularizer. Our interest is in big-data problems
wherein there is a large number of variables to optimize. If treated by means
of standard distributed optimization algorithms, these large-scale problems may
be intractable, due to the prohibitive local computation and communication
burden at each node. We propose a novel distributed solution method whereby at
each iteration agents optimize and then communicate (in an uncoordinated
fashion) only a subset of their decision variables. To deal with non-convexity
of the cost function, the novel scheme hinges on Successive Convex
Approximation (SCA) techniques coupled with i) a tracking mechanism
instrumental to locally estimate gradient averages; and ii) a novel block-wise
consensus-based protocol to perform local block-averaging operations and
gradient tacking. Asymptotic convergence to stationary solutions of the
nonconvex problem is established. Finally, numerical results show the
effectiveness of the proposed algorithm and highlight how the block dimension
impacts on the communication overhead and practical convergence speed
Constrained Optimal Consensus in Multi-agent Systems with First and Second Order Dynamics
This paper fully studies distributed optimal consensus problem in
non-directed dynamical networks. We consider a group of networked agents that
are supposed to rendezvous at the optimal point of a collective convex
objective function. Each agent has no knowledge about the global objective
function and only has access to its own local objective function, which is a
portion of the global one, and states information of agents within its
neighborhood set. In this setup, all agents coordinate with their neighbors to
seek the consensus point that minimizes the networks global objective function.
In the current paper, we consider agents with single-integrator and
double-integrator dynamics. We further suppose that agents movements are
limited by some convex inequality constraints. In order to find the optimal
consensus point under the described scenario, we combine the interior-point
optimization algorithm with a consensus protocol and propose a distributed
control law. The associated convergence analysis based on Lyapunov stability
analysis is provided
Distributed Subgradient Projection Algorithm over Directed Graphs: Alternate Proof
We propose Directed-Distributed Projected Subgradient (D-DPS) to solve a
constrained optimization problem over a multi-agent network, where the goal of
agents is to collectively minimize the sum of locally known convex functions.
Each agent in the network owns only its local objective function, constrained
to a commonly known convex set. We focus on the circumstance when
communications between agents are described by a \emph{directed} network. The
D-DPS combines surplus consensus to overcome the asymmetry caused by the
directed communication network. The analysis shows the convergence rate to be
.Comment: Disclaimer: This manuscript provides an alternate approach to prove
the results in \textit{C. Xi and U. A. Khan, Distributed Subgradient
Projection Algorithm over Directed Graphs, in IEEE Transactions on Automatic
Control}. The changes, colored in blue, result into a tighter result in
Theorem~1". arXiv admin note: text overlap with arXiv:1602.0065
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
Continuous-time Proportional-Integral Distributed Optimization for Networked Systems
In this paper we explore the relationship between dual decomposition and the
consensus-based method for distributed optimization. The relationship is
developed by examining the similarities between the two approaches and their
relationship to gradient-based constrained optimization. By formulating each
algorithm in continuous-time, it is seen that both approaches use a gradient
method for optimization with one using a proportional control term and the
other using an integral control term to drive the system to the constraint set.
Therefore, a significant contribution of this paper is to combine these methods
to develop a continuous-time proportional-integral distributed optimization
method. Furthermore, we establish convergence using Lyapunov stability
techniques and utilizing properties from the network structure of the
multi-agent system.Comment: 23 Pages, submission to Journal of Control and Decision, under
review. Takes comments from previous review process into account. Reasons for
a continuous approach are given and minor technical details are remedied.
Largest revision is reformatting for the Journal of Control and Decisio
Robust Consensus of Linear Multi-Agent Systems under Input Constraints or Uncertainties
This paper proposes a new approach to analyze and synthesize robust consensus
control laws for general linear leaderless multi-agent systems (MASs) subjected
to input constraints or uncertainties. First, the MAS under input constraints
or uncertainties is reformulated as a network of Lur'e systems. Next, two
scenarios of communication topology are considered, namely undirected and
directed cyclic structures. In each case, a sufficient condition for consensus
and the design of consensus controller gain are derived from solutions of a
distributed LMI convex problem. Finally, a numerical example is introduced to
illustrate the effectiveness of the proposed theoretical approach.Comment: submitted to Automatica. arXiv admin note: text overlap with
arXiv:1605.0364
Initialization-free Distributed Algorithms for Optimal Resource Allocation with Feasibility Constraints and its Application to Economic Dispatch of Power Systems
In this paper, the distributed resource allocation optimization problem is
investigated. The allocation decisions are made to minimize the sum of all the
agents' local objective functions while satisfying both the global network
resource constraint and the local allocation feasibility constraints. Here the
data corresponding to each agent in this separable optimization problem, such
as the network resources, the local allocation feasibility constraint, and the
local objective function, is only accessible to individual agent and cannot be
shared with others, which renders new challenges in this distributed
optimization problem. Based on either projection or differentiated projection,
two classes of continuous-time algorithms are proposed to solve this
distributed optimization problem in an initialization-free and scalable manner.
Thus, no re-initialization is required even if the operation environment or
network configuration is changed, making it possible to achieve a
"plug-and-play" optimal operation of networked heterogeneous agents. The
algorithm convergence is guaranteed for strictly convex objective functions,
and the exponential convergence is proved for strongly convex functions without
local constraints. Then the proposed algorithm is applied to the distributed
economic dispatch problem in power grids, to demonstrate how it can achieve the
global optimum in a scalable way, even when the generation cost, or system
load, or network configuration, is changing.Comment: 13 pages, 7 figure
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