A new efficient primal-dual decomposition algorithm for nonconvex optimization with separable structures

A primal-dual decomposition algorithm that is a result of the authors´ continued efforts toward solving nonconvex constrained optimization problems with separable structures is presented. This algorithm involves no matrix inverse in penalty terms, so it is more computationally efficient than existing algorithms. The new algorithm is shown to have a linear rate of convergence. Numerical examples are also provided. This algorithm will be valuable for generalizing the primal-dual decomposition approach from equality-constrained to inequality-constrained optimization problems