## 2014

# An Extesion of the Method of Multipliers for Distributed Nonlinear Programming

Ion Matei, John S. Baras, Marzieh Nabi and Tolga Kurtoglu

*To appear in the Proceedings of the 51st IEEE Conference on Decision Control (CDC 2014),
*Los Angeles, CA, 15-17 December, 2014.

**Abstract**

In this paper we consider a distributed optimization problem, where a set of agents interacting through a communication graph have as common goal the minimization of a function expressed as a sum of (possibly non-convex) differentiable functions. Each function in the sum corresponds to an agent and each agent has associated an equality constraint. The majority of distributed optimization algorithms in the literature are based on first-order numerical methods. In this paper we investigate how the method of multipliers can be used to solve an optimization problem with equality constraints in a distributed manner. The method of multipliers is applied to a lifted optimization problem whose solution embeds the solution of the original problem. We modify the standard convergence results for the method of multipliers to deal with the fact the (local) minimizers of the lifted optimization problem are not regular, as a results of the distributed formulation. Practical distributed implementation aspects are also addressed.