Global Optimization: A Distributed Compensation Algorithm and its Convergence Analysis

This paper introduces a distributed compensation approach for the global optimization with separable objective functions and coupled constraints. By employing compensation variables, the global optimization problem can be solved without the information exchange of coupled constraints. The convergence analysis of the proposed algorithm is presented with the convergence condition through which a diminishing step-size with an upper bound can be determined. The convergence rate can be achieved at $O({lnT}/{\sqrt {T}})$ . Moreover, the equilibrium of this algorithm is proved to converge at the optimal solution of the global optimization problem. The effectiveness and the practicability of the proposed algorithm is demonstrated by the parameter optimization problem in smart building.