A New Technique for Nonconvex Primal-Dual Decomposition of a Large-Scale Separable Optimization Problem

The primal-dual approach is quite effective in decomposing a convex separable optimization problem into several subproblems of smaller sizes. In this paper, we present a new technique which extends the primal-dual approach to nonconvex problems. Since a straightforward application of the so-called multiplier method destroys separability, a new Lagrangian function is proposed here which preserves separability. Based on this new function we develop a new iterative method for finding an optimal solution to the problem and show that the method is locally convergent to an optimal solution. Furthermore, the effect of certain parameters on the ratio of convergence is investigated and a simple example is given to illustrate the proposed approach.