A distributed algorithm for cooperative optimization with polynomial objective function

In this paper, we focus on designing a distributed algorithm for solving a kind of unconstrained cooperative optimization problem with polynomial objective function subject to variable coupling. A Lasserre relaxation method is used to convert the studied cooperative optimization problem to an equivalent semi-definite programming problem. Underlying the knowledge of graph theory, we disassemble variables of connection matrix and introduce a distributed alternating directions method of multipliers to solve the semi-definite programming problem. Different from the existing results, the advantage of the introduced algorithm is that it gives a distributed computing way to solve a kind of cooperative optimization problem with objective function subject to variable coupling. Finally, two simulation examples are given to verify the effectiveness of the proposed algorithm.