## 2013

# Distributed Algorithms for Optimization Problems with Equality Constraints

I. Matei and J. S. Baras

*Proceedings of the 52nd IEEE Conference on Decision and Control, *pp. 2352-2357, Firenze, Italy, December 10-13, 2013.

**Abstract**

In this paper we introduce two discrete-time, distributed optimization algorithms executed by a set of agents whose interactions are subject to a communication graph. The algorithms can be applied to optimization problems where the cost function is expressed as a sum of functions, and where each function is associated to an agent. In addition, the agents can have equality constraints as well. The algorithms are not consensus-based and can be applied to non-convex optimization problems with equality constraints. We demonstrate that the first distributed algorithm results naturally from applying a first order method to solve the first order necessary conditions for a lifted optimization problem with equality constraints; the solution of our original problem is embedded in the solution of this lifted optimization problem. Using an augmented Lagrangian idea, we derive a second distributed algorithm that requires weaker conditions for local convergence compared to the first algorithm. For both algorithms we address the local convergence properties.