Decomposition algorithms for large-scale nonconvex optimization problems

In order for primal-dual methods to be applicable to a constrained minimization problem it is necessary that restrictive convexity conditions are satisfied. In this paper we consider a procedure by means of which a nonconvex problem is convexified and transformed into one which can be solved with the aid of primal-dual methods. Under this transformation, separability of the type necessary for application of decomposition algorithms is preserved. This feature extends the range of applicability of such algorithms to nonconvex problems.