Distributed Global Optimization for a Class of Nonconvex Optimization With Coupled Constraints

This article examines the distributed nonconvex optimization problem with structured nonconvex objective functions and coupled convex inequality constraints on static networks. A distributed continuous-time primal-dual algorithm is proposed to solve the problem. We use the canonical transformation and Lagrange multiplier method to reformulate the nonconvex optimization problem as a convex-concave saddle point computation problem, which is subsequently solved by employing the projected primal-dual subgradient method. Sufficient conditions that guarantee the global optimality of the solution generated by the proposed algorithm are provided. Numerical and application examples are presented to demonstrate the proposed algorithm.