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## Constrained consensus and optimization in multi-agent networks (2008)

Venue: | IEEE TRANSACTIONS ON AUTOMATIC CONTROL |

Citations: | 109 - 8 self |

### Citations

5217 | Convex Analysis
- Rockafellar
- 1970
(Show Context)
Citation Context ... keep our discussion general, we do not assume differentiability of any of the functions fi. Since each fi is convex over the entire R n , the function is differentiable almost everywhere (see [2] or =-=[25]-=-). At the points where the function fails to be differentiable, a subgradient exists and can be used in the role of a gradient. In particular, for a given convex function F : R n → R and a point ¯x, a... |

1271 |
Theory of reproducing kernels
- Aronszajn
- 1950
(Show Context)
Citation Context ...s by projecting iteratively on the sets (either cyclically or with some given order), see Figure 2(a). The convergence behavior of these methods has been established by Von Neumann [20] and Aronszajn =-=[1]-=- for the case when the sets Xi are affine; and by Gubin et al. [11] when the sets Xi are closed and convex. Gubin et al. [11] also have provided convergence rate results for a particular form of alter... |

1213 | Coordination of groups of mobile autonomous agents using nearest neighbor rules,”
- Jadbabaie, Lin, et al.
- 2003
(Show Context)
Citation Context ...bjective function at each processor). More recent literature focused on multi-agent environments and studied consensus algorithms for achieving cooperative behavior in a distributed manner (see [28], =-=[12]-=-, [6], [21], [7], and [22, 23]). These works assume that the agent values can be processed arbitrarily and are unconstrained. Another recent approach for distributed cooperative control problems invol... |

1029 | Consensus problems in networks of agents with switching topology and timedelays
- Olfati-Saber, Murray
- 2004
(Show Context)
Citation Context ...nction at each processor). More recent literature focused on multi-agent environments and studied consensus algorithms for achieving cooperative behavior in a distributed manner (see [28], [12], [6], =-=[21]-=-, [7], and [22, 23]). These works assume that the agent values can be processed arbitrarily and are unconstrained. Another recent approach for distributed cooperative control problems involve using ga... |

941 |
Tsitsiklis, Parallel and distributed computation: numerical methods. Upper Saddle River
- Bertsekas, N
- 1989
(Show Context)
Citation Context ...terates to the intersection set. Related literature on parallel and distributed computation is vast. Most literature builds on the seminal work of Tsitsiklis [26] and Tsitsiklis et al. [27] (see also =-=[3]-=-), which focused on distributing the computations involved with optimizing a global objective function among different processors (assuming complete information about the global objective function at ... |

389 |
Distributed asynchronous deterministic and stochastic gradient optimization algorithms
- Tsitsiklis, Bertsekas, et al.
- 1986
(Show Context)
Citation Context ...tances of the iterates to the intersection set. Related literature on parallel and distributed computation is vast. Most literature builds on the seminal work of Tsitsiklis [26] and Tsitsiklis et al. =-=[27]-=- (see also [3]), which focused on distributing the computations involved with optimizing a global objective function among different processors (assuming complete information about the global objectiv... |

295 |
Convex Analysis and Optimization. Athena Scientific
- Bertsekas, Nedić, et al.
- 2003
(Show Context)
Citation Context .... 20To keep our discussion general, we do not assume differentiability of any of the functions fi. Since each fi is convex over the entire R n , the function is differentiable almost everywhere (see =-=[2]-=- or [25]). At the points where the function fails to be differentiable, a subgradient exists and can be used in the role of a gradient. In particular, for a given convex function F : R n → R and a poi... |

235 |
Problems in decentralized decision making and computation
- Tsitsiklis
- 1984
(Show Context)
Citation Context ...onstraint sets with the distances of the iterates to the intersection set. Related literature on parallel and distributed computation is vast. Most literature builds on the seminal work of Tsitsiklis =-=[26]-=- and Tsitsiklis et al. [27] (see also [3]), which focused on distributing the computations involved with optimizing a global objective function among different processors (assuming complete informatio... |

219 | Gossip algorithms: Design, analysis and applications. Pages 1653–1664 of: Infocom 2005. 24th annual joint conference of the ieee computer and communications societies. proceedings ieee
- Boyd, Ghosh, et al.
- 2005
(Show Context)
Citation Context ...ve function at each processor). More recent literature focused on multi-agent environments and studied consensus algorithms for achieving cooperative behavior in a distributed manner (see [28], [12], =-=[6]-=-, [21], [7], and [22, 23]). These works assume that the agent values can be processed arbitrarily and are unconstrained. Another recent approach for distributed cooperative control problems involve us... |

218 |
Finite-Dimensional Variational Inequalities and Complementarity Problems, ser
- Pang, Facchinei
- 2003
(Show Context)
Citation Context ...negative gradient of its own objective function fi = 1 2 ‖x − PXi‖2 at x = ∑m j=1 aij (k)xj(k). In particular, since the gradient of fi is ∇fi(x) = x −PXi [x] (see Theorem 1.5.5 in Facchinei and Pang =-=[10]-=-), the update rule in Eq. (3) is equivalent to the following gradient descent method for minimizing fi: x i m∑ (k + 1) = a i j (k)xj ( m∑ [ m∑ (k) − a i j (k)xj ]) (k) . j=1 j=1 a i j (k)xj (k) − PXi ... |

128 | Tsitsiklis, Distributed averaging algorithms and quantization effects. http://arxiv.org/abs/0803.1202
- Nedić, Olshevsky, et al.
- 2008
(Show Context)
Citation Context ...tly infinitely many times exchange information at least once every B time slots. 2 2 It is possible to adopt weaker connectivity assumptions for the multi-agent model as those used in the recent work =-=[16]-=-. 103.4 Transition Matrices We introduce matrices A(s), whose i-th column is the weight vector a i (s), and the matrices where Φ(k, s) = A(s)A(s + 1) · · ·A(k − 1)A(k) for all s and k with k ≥ s, Φ(k... |

124 |
The method of projections for finding the common point of convex sets
- Gubin, Polyak, et al.
- 1967
(Show Context)
Citation Context ... some given order), see Figure 2(a). The convergence behavior of these methods has been established by Von Neumann [20] and Aronszajn [1] for the case when the sets Xi are affine; and by Gubin et al. =-=[11]-=- when the sets Xi are closed and convex. Gubin et al. [11] also have provided convergence rate results for a particular form of alternating projection method. Similar rate results under different assu... |

92 |
Products of indecomposable, aperiodic, stochastic matrices
- Wolfowitz
- 1963
(Show Context)
Citation Context ...gent estimates associated with the algorithms introduced in Sections 3 and 4. The convergence properties of these matrices as k → ∞ have been extensively studied and well-established (see [26], [12], =-=[29]-=-). Under the assumptions of Section 3.3, the matrices Φ(k, s) converge as k → ∞ to a uniform steady state distribution for each s at a geometric rate, i.e., limk→∞ Φ(k, s) = 1 m ee′ for all s. The fac... |

59 | A convergent incremental gradient method with constant step size
- Blatt, Hero, et al.
- 2007
(Show Context)
Citation Context ...main focus in this paper. Our work is also related to incremental subgradient algorithms implemented over a network, where agents sequentially update an iterate sequence in a cyclic or a random order =-=[4, 15, 24, 13]-=-. In an incremental algorithm, there is a single iterate sequence and only one agent updates the iterate at a given time. Thus, while operating on the basis of local information, incremental algorithm... |

54 |
Convergence rates in distributed consensus and averaging
- Olshevsky, Tsitsiklis
- 2006
(Show Context)
Citation Context ...processor). More recent literature focused on multi-agent environments and studied consensus algorithms for achieving cooperative behavior in a distributed manner (see [28], [12], [6], [21], [7], and =-=[22, 23]-=-). These works assume that the agent values can be processed arbitrarily and are unconstrained. Another recent approach for distributed cooperative control problems involve using game-theoretic models... |

47 | Incremental stochastic sub-gradient algorithms for convex optimization,” Available at http://arxiv.org/abs/0806.1092
- Ram, Nedić, et al.
- 2008
(Show Context)
Citation Context ...main focus in this paper. Our work is also related to incremental subgradient algorithms implemented over a network, where agents sequentially update an iterate sequence in a cyclic or a random order =-=[4, 15, 24, 13]-=-. In an incremental algorithm, there is a single iterate sequence and only one agent updates the iterate at a given time. Thus, while operating on the basis of local information, incremental algorithm... |

40 | A lower bound on convergence of a distributed network consencus algorithm
- Cao, Spielman, et al.
- 2005
(Show Context)
Citation Context ... at each processor). More recent literature focused on multi-agent environments and studied consensus algorithms for achieving cooperative behavior in a distributed manner (see [28], [12], [6], [21], =-=[7]-=-, and [22, 23]). These works assume that the agent values can be processed arbitrarily and are unconstrained. Another recent approach for distributed cooperative control problems involve using game-th... |

36 |
Rate of convergence of the method of alternating projections,” in Parametric Optimization and Approximation
- Deutsch
- 1983
(Show Context)
Citation Context ...bin et al. [11] also have provided convergence rate results for a particular form of alternating projection method. Similar rate results under different assumptions have also been provided by Deutsch =-=[8]-=-, and Deutsch and Hundal [9]. The constrained consensus algorithm [cf. Eq. (3)] generates a sequence of iterates for each agent as follows: at iteration k, each agent i first forms a linear combinatio... |

36 | Connections between cooperative control and potential games illustrated on the consensus problem
- Marden, Arslan, et al.
- 2007
(Show Context)
Citation Context ...ibrium which is the same as or close to a global optimum. Various learning algorithms can then be used as distributed control schemes that will reach the equilibrium. In a recent paper, Marden et al. =-=[14]-=- used this approach for the consensus problem where agents have constraints on their values. Our projected consensus algorithm provides an alternative approach for this problem. Most closely related t... |

25 |
H.: The rate of convergence for the cyclic projections algorithm iii: Regularity of convex sets
- Deutsch, Hundal
(Show Context)
Citation Context ...ovided convergence rate results for a particular form of alternating projection method. Similar rate results under different assumptions have also been provided by Deutsch [8], and Deutsch and Hundal =-=[9]-=-. The constrained consensus algorithm [cf. Eq. (3)] generates a sequence of iterates for each agent as follows: at iteration k, each agent i first forms a linear combination 1 We focus throughout the ... |

21 |
A simple peer-to-peer algorithm for distributed optimization in sensor networks
- Johansson, Rabi, et al.
(Show Context)
Citation Context ...main focus in this paper. Our work is also related to incremental subgradient algorithms implemented over a network, where agents sequentially update an iterate sequence in a cyclic or a random order =-=[4, 15, 24, 13]-=-. In an incremental algorithm, there is a single iterate sequence and only one agent updates the iterate at a given time. Thus, while operating on the basis of local information, incremental algorithm... |

13 |
subgradient methods for multi-agent optimization
- Distributed
(Show Context)
Citation Context ...nsus problem where agents have constraints on their values. Our projected consensus algorithm provides an alternative approach for this problem. Most closely related to our work are the recent papers =-=[18, 17]-=-, which proposed distributed subgradient methods for solving unconstrained multi-agent optimization problems. These methods use consensus algorithms as a mechanism for distributing computations among ... |

11 |
I Cohen and O Schochet, Novel type of phase transitions in a system of self-driven particles
- Vicsek, Czirok, et al.
- 1995
(Show Context)
Citation Context ...obal objective function at each processor). More recent literature focused on multi-agent environments and studied consensus algorithms for achieving cooperative behavior in a distributed manner (see =-=[28]-=-, [12], [6], [21], [7], and [22, 23]). These works assume that the agent values can be processed arbitrarily and are unconstrained. Another recent approach for distributed cooperative control problems... |

10 |
Functional operators I
- Neumann
- 1950
(Show Context)
Citation Context ... sequence of vectors by projecting iteratively on the sets (either cyclically or with some given order), see Figure 2(a). The convergence behavior of these methods has been established by Von Neumann =-=[20]-=- and Aronszajn [1] for the case when the sets Xi are affine; and by Gubin et al. [11] when the sets Xi are closed and convex. Gubin et al. [11] also have provided convergence rate results for a partic... |

8 | Tsitsiklis, Distributed subgradient algorithms and quantization effects - Nedić, Olshevsky, et al. |

5 |
methods for saddle-point problems
- “Subgradient
- 2009
(Show Context)
Citation Context ...ual” subgradient algorithms, in which dual variables (or prices) are used to ensure feasibility of agent estimates with respect to global constraints. Such algorithms have been studied in recent work =-=[19]-=- for general convex constrained optimization problems (without a multi-agent network structure). Moreover, in this paper, we presented convergence results for the distributed subgradient algorithm for... |

1 |
On the rate of convergence of distributed subradient methods for multi-agent optimization
- Nedić, Ozdaglar
- 2007
(Show Context)
Citation Context ...nsus problem where agents have constraints on their values. Our projected consensus algorithm provides an alternative approach for this problem. Most closely related to our work are the recent papers =-=[18, 17]-=-, which proposed distributed subgradient methods for solving unconstrained multi-agent optimization problems. These methods use consensus algorithms as a mechanism for distributing computations among ... |