Cooperative optimisation with inseparable cost functions

Cooperative optimisation problems over multi-agent systems have attracted a lot of attention. Most of existing results have been developed for the case when a cost function is given as a summation of local utilities. Instead, this study focuses on a more general case when the cost function is not given as a summation form or cannot be readily changed into a summation form. The authors call this case as the cooperative optimisation with inseparable cost functions. The authors´ basic idea is to decompose the inseparable cost function into local utilities based on geometric theory. Each of the decomposed agent optimisation problems only contains its own variable and constraints, and a gradient projection algorithm is proposed to solve the obtained distributed optimisation problem. It is further shown that the proposed algorithm converges and its solution coincides with the globally optimal solution under certain conditions, such as convexity of the cost function. Finally, two examples are given to illustrate the method.