A new class of distributed optimization algorithms: application to regression of distributed data

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.

Keywords:

• distributed optimization
• convex optimization
• distributed regression

AMS Subject Classification :

• 90C25
• 90C30

Acknowledgements

This work has been supported by NSF Career Grant CMMI 07-42538.

Notes

There is no loss of generality in fixing the number of observations to be m.