Distributed optimization with unconstrained polynomial objective function

Distributed optimization has been proposed for parallel computing for many years. At present, many distributed algorithms are developed for solving the cooperative optimization problem of multi-agent systems with objective function in summation form of local utilities. In order to solve more general optimization problems in a distributed way, in this paper, we study the distributed optimization problem with unconstrained polynomial objective function and use the Lasserre's relaxation method to convert the studied optimization problem to an equivalent semidefinite programming. Underlying the knowledge of graph theory, we disassemble the matrix variables and propose a distributed alternating directions method of multipliers to solve the semidefinite programming. Finally, a numerical example is used to illustrate the feasibility of our proposed algorithm.