### Abstract

We consider distributed optimization by a collection of nodes, each having access to its own convex function, whose collective goal is to minimize the sum of the functions. The communications between nodes are described by a time-varying sequence of directed graphs, which is uniformly strongly connected. For such communications, assuming that every node knows its out-degree, we develop a broadcast-based algorithm, termed the subgradient-push, which steers every node to an optimal value under a standard assumption of subgradient boundedness. The subgradient-push requires no knowledge of either the number of agents or the graph sequence to implement. Our analysis shows that the subgradient-push algorithm converges at a rate of O(ln t/√t). The proportionality constant in the convergence rate depends on the initial values at the nodes, the subgradient norms and, more interestingly, on both the speed of the network information diffusion and the imbalances of influence among the nodes.

Original language | English (US) |
---|---|

Article number | 6930814 |

Pages (from-to) | 601-615 |

Number of pages | 15 |

Journal | IEEE Transactions on Automatic Control |

Volume | 60 |

Issue number | 3 |

DOIs | |

State | Published - Mar 1 2015 |

Externally published | Yes |

### Fingerprint

### Keywords

- Time-varying
- UAVs

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Control and Systems Engineering
- Computer Science Applications

### Cite this

*IEEE Transactions on Automatic Control*,

*60*(3), 601-615. [6930814]. https://doi.org/10.1109/TAC.2014.2364096

**Distributed optimization over time-varying directed graphs.** / Nedich, Angelia; Olshevsky, Alex.

Research output: Contribution to journal › Article

*IEEE Transactions on Automatic Control*, vol. 60, no. 3, 6930814, pp. 601-615. https://doi.org/10.1109/TAC.2014.2364096

}

TY - JOUR

T1 - Distributed optimization over time-varying directed graphs

AU - Nedich, Angelia

AU - Olshevsky, Alex

PY - 2015/3/1

Y1 - 2015/3/1

N2 - We consider distributed optimization by a collection of nodes, each having access to its own convex function, whose collective goal is to minimize the sum of the functions. The communications between nodes are described by a time-varying sequence of directed graphs, which is uniformly strongly connected. For such communications, assuming that every node knows its out-degree, we develop a broadcast-based algorithm, termed the subgradient-push, which steers every node to an optimal value under a standard assumption of subgradient boundedness. The subgradient-push requires no knowledge of either the number of agents or the graph sequence to implement. Our analysis shows that the subgradient-push algorithm converges at a rate of O(ln t/√t). The proportionality constant in the convergence rate depends on the initial values at the nodes, the subgradient norms and, more interestingly, on both the speed of the network information diffusion and the imbalances of influence among the nodes.

AB - We consider distributed optimization by a collection of nodes, each having access to its own convex function, whose collective goal is to minimize the sum of the functions. The communications between nodes are described by a time-varying sequence of directed graphs, which is uniformly strongly connected. For such communications, assuming that every node knows its out-degree, we develop a broadcast-based algorithm, termed the subgradient-push, which steers every node to an optimal value under a standard assumption of subgradient boundedness. The subgradient-push requires no knowledge of either the number of agents or the graph sequence to implement. Our analysis shows that the subgradient-push algorithm converges at a rate of O(ln t/√t). The proportionality constant in the convergence rate depends on the initial values at the nodes, the subgradient norms and, more interestingly, on both the speed of the network information diffusion and the imbalances of influence among the nodes.

KW - Time-varying

KW - UAVs

UR - http://www.scopus.com/inward/record.url?scp=84923608183&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84923608183&partnerID=8YFLogxK

U2 - 10.1109/TAC.2014.2364096

DO - 10.1109/TAC.2014.2364096

M3 - Article

VL - 60

SP - 601

EP - 615

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 0018-9286

IS - 3

M1 - 6930814

ER -