Penalty dual decomposition method with application in signal processing

Many problems of recent interest in signal processing, machine learning and wireless communications can be posed as nonconvex nonsmooth optimization problems. These problems are generally difficult to solve especially when the optimization variables are nonlinearly coupled in some nonconvex constraints. In this paper, we propose an algorithm named “penalty dual decomposition” (PDD) method, for the minimization of a nonconvex nonsmooth objective subject to nonconvex constraints. We show that the PDD converges to KKT solutions under certain constraint qualification condition. Simulations corroborate the excellent performance of the PDD method.