### Abstract

In a distributed optimization problem, the complete problem information is not available at a single location but is rather distributed among different agents in a multi-agent system. In the problems studied in the literature, each agent has an objective function and the network goal is to minimize the sum of the agents objective functions over a constraint set that is globally known. In this paper, we study a generalization of the above distributed optimization problem. In particular, the network objective is to minimize a function of the sum of the individual objective functions over the constraint set. The outer function and the constraint set are known to all the agents. We discuss an algorithm and prove its convergence, and then discuss extensions to more general and complex distributed optimization problems. We provide a motivation for our algorithms through the example of distributed regression of distributed data.

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

Pages (from-to) | 71-88 |

Number of pages | 18 |

Journal | Optimization Methods and Software |

Volume | 27 |

Issue number | 1 |

DOIs | |

State | Published - Feb 1 2012 |

Externally published | Yes |

### Fingerprint

### Keywords

- convex optimization
- distributed optimization
- distributed regression

### ASJC Scopus subject areas

- Control and Optimization
- Software
- Applied Mathematics

### Cite this

*Optimization Methods and Software*,

*27*(1), 71-88. https://doi.org/10.1080/10556788.2010.511669

**A new class of distributed optimization algorithms : Application to regression of distributed data.** / Sundhar Ram, S.; Nedich, Angelia; Veeravalli, V. V.

Research output: Contribution to journal › Article

*Optimization Methods and Software*, vol. 27, no. 1, pp. 71-88. https://doi.org/10.1080/10556788.2010.511669

}

TY - JOUR

T1 - A new class of distributed optimization algorithms

T2 - Application to regression of distributed data

AU - Sundhar Ram, S.

AU - Nedich, Angelia

AU - Veeravalli, V. V.

PY - 2012/2/1

Y1 - 2012/2/1

N2 - In a distributed optimization problem, the complete problem information is not available at a single location but is rather distributed among different agents in a multi-agent system. In the problems studied in the literature, each agent has an objective function and the network goal is to minimize the sum of the agents objective functions over a constraint set that is globally known. In this paper, we study a generalization of the above distributed optimization problem. In particular, the network objective is to minimize a function of the sum of the individual objective functions over the constraint set. The outer function and the constraint set are known to all the agents. We discuss an algorithm and prove its convergence, and then discuss extensions to more general and complex distributed optimization problems. We provide a motivation for our algorithms through the example of distributed regression of distributed data.

AB - In a distributed optimization problem, the complete problem information is not available at a single location but is rather distributed among different agents in a multi-agent system. In the problems studied in the literature, each agent has an objective function and the network goal is to minimize the sum of the agents objective functions over a constraint set that is globally known. In this paper, we study a generalization of the above distributed optimization problem. In particular, the network objective is to minimize a function of the sum of the individual objective functions over the constraint set. The outer function and the constraint set are known to all the agents. We discuss an algorithm and prove its convergence, and then discuss extensions to more general and complex distributed optimization problems. We provide a motivation for our algorithms through the example of distributed regression of distributed data.

KW - convex optimization

KW - distributed optimization

KW - distributed regression

UR - http://www.scopus.com/inward/record.url?scp=84855928432&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84855928432&partnerID=8YFLogxK

U2 - 10.1080/10556788.2010.511669

DO - 10.1080/10556788.2010.511669

M3 - Article

AN - SCOPUS:84855928432

VL - 27

SP - 71

EP - 88

JO - Optimization Methods and Software

JF - Optimization Methods and Software

SN - 1055-6788

IS - 1

ER -