Hierarchical optimization of the power-decentralized system, in which a central system and plural regional systems (subsystems) possess their own objective functions, is considered. The lower level consists of N regional systems each of which possesses its own decision variable vector, objective function, and constraint conditions. The central system in the higher level has the function of coordinating the regional systems through resource allocation, while the subsystems optimize their own objectives using given resources. The purpose of this study is to prescribe a new solution method for such a general resource allocation problem. A method is proposed in which a nonlinear programming problem approximating the original hierarchical one is solved iteratively by applying the penalty function method to the lower level problems. It is proved that a sequence of approximated solutions converges to the optimal solution. Some examples demonstrate the effectiveness of the proposed algorithm.
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