Distributed algorithms for sparse, large-scale optimization problems are preferable over centralized solvers whenthe computational units are physically far apart from each other or the problem size is too large for the available memory. However, most distributed methods sacrifice convergence speed for simpler computations. In this paper, we propose a novel algorithm for a certain class of nonconvex, separable optimization problems that combines both distributed computations and locally quadratic convergence. It is based on the principle of primal decomposition with exact Hessian information but uses soft coupling between the agents to avoid global calculations and adapt faster to online data changes. An important application field of the presented method is nonlinear parameter estimation, where increasing the number of experiments may lead to problem dimensions that are prohibitive for conventional solvers. We assess the performance of our method on the identification of an Airborne Wind Energy (AWE) system using real-world experimental data.