Distributed Nonlinear Programming Methods for Optimization Problems with Inequality Constraints

In this paper, we consider a distributed optimization problem, where a set of agents interacting and cooperating locally have as common goal the minimization of a function expressed as a sum of (possibly non-convex) differentiable functions. Each function in the sum is associated with an agent and each agent has assigned an inequality constraint, therefore generating an optimization problem with inequality constraints. In this paper, we present a distributed algorithm for solving such a problem and give local convergence results. Our approach is based on solving (in a centralized manner) an equivalent augmented optimization problem with mixed constraints. The structure of this augmented problem ensures that the resulting algorithm is distributed. The main challenge in proving the convergence results comes from the fact that the local minimizers are no longer regular due to the distributed formulation. We present also an extension of this algorithm that solves a constrained optimization problem, where each agent has both equality and inequality constraints.