Distributed Algorithm via Continuously Differentiable Exact Penalty Method for Network Optimization

Abstract

This paper proposes a distributed optimization framework for solving nonlinear programming problems with separable objective function and local constraints. Our novel approach is based on first reformulating the original problem as an unconstrained optimization problem using continuously differentiable exact penalty function methods and then using gradient based optimization algorithms. The reformulation is based on replacing the Lagrange multipliers in the augmented Lagrangian of the original problem with Lagrange multiplier functions. The problem of calculating the gradient of the penalty function is challenging as it is non-distributed in general even if the original problem is distributed. We show that we can reformulate this problem as a distributed, unconstrained convex optimization problem. The proposed framework opens new opportunities for the application of various distributed algorithms designed for unconstrained optimization.