Distributed nonconvex optimization over networks

Paolo Di Lorenzo, Gesualdo Scutari

Abstract: We study nonconvex distributed optimization in multi-agent networks. We introduce a novel algorithmic framework for the distributed minimization of the sum of a smooth (possibly nonconvex) function-the agents' sum-utility-plus a convex (possibly nonsmooth) regularizer. The proposed method hinges on successive convex approximation (SCA) techniques while leveraging dynamic consensus as a mechanism to distribute the computation among the agents. Asymptotic convergence to (stationary) solutions of the nonconvex problem is established. Numerical results show that the new method compares favorably to existing algorithms on both convex and nonconvex problems.