Distributed Optimization Methods for Nonconvex Problems with Inequality Constraints over Time-Varying Networks

Network-structured optimization problems are found widely in engineering applications. In this paper, we investigate a nonconvex distributed optimization problem with inequality constraints associated with a time-varying multiagent network, in which each agent is allowed to locally access its own cost function and collaboratively minimize a sum of nonconvex cost functions for all the agents in the network. Based on successive convex approximation techniques, we first approximate locally the nonconvex problem by a sequence of strongly convex constrained subproblems. In order to realize distributed computation, we then exploit the exact penalty function method to transform the sequence of convex constrained subproblems into unconstrained ones. Finally, a fully distributed method is designed to solve the unconstrained subproblems. The convergence of the proposed algorithm is rigorously established, which shows that the algorithm can converge asymptotically to a stationary solution of the problem under consideration. Several simulation results are illustrated to show the performance of the proposed method.