  In this paper we investigate how standard nonlinear programming algorithms
can be used to solve constrained optimization problems in a distributed manner.
The optimization setup consists of a set of agents interacting through a
communication graph that 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. By re-casting the distributed optimization problem into an
equivalent, augmented centralized problem, we show that distributed algorithms
result naturally from applying standard nonlinear programming techniques. Due
to the distributed formulation, the standard assumptions and convergence
results no longer hold. We emphasize what changes are necessary for convergence
to still be achieved for three algorithms: two algorithms based on Lagrangian
methods, and an algorithm based the method of multipliers. The changes in the
convergence results are necessary mainly due to the fact that the (local)
minimizers of the lifted optimization problem are not regular, as a results of
the distributed formulation. Unlike the standard algorithm based on the method
of multipliers, for the distributed version we cannot show that the theoretical
superlinear convergence rate can be achieved.

Optimization and Control