階層分権システムの障壁法による新しい解法

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  • Hierarchical Decentralized System and Its New Solution Method by a Barrier Method
  • 段層分権システムの障壁法による新しい解法
  • ダンソウ ブンケン システム ノ ショウヘキホウ ニヨル アタラシイ カイホウ

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We study on hierarchical optimization of the power-decentralized system, in which a central system and plural regional systems (subsystems) possess their own objective functions. 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 a function of coordinating the regional systems. The basic principle of planning is that the central system allocates resources so as to optimize its own objective, while the subsystems optimize their own objective using the given resources. Accordingly, the respective subsystem generates an optimal parametric solution w. r. t. the given resource. The central decision-maker, then, chooses an optimal resource allocation based on knowledge about subsystems' behavior. Such problems with precedence in decisive powers can be solved in principle by a parametric approach.<br>In the past, most studies of two-level planning were limited to the cases in which the central objective is a function of subsystems' objectives. By use of directional derivatives, then, nondifferentiable programming was applied to improve resource allocation successively.<br>In this paper, we are concerned with the cases in which the central objective consists of subsystems' optimal parametric solutions generally. Such problem is regarded as the most general resource allocation problem.<br>A new computational method is proposed such that a nonlinear programming problem approximating the original hierarchical one is solved iteratively by applying a penalty function method to the lower level problems. It is proved that a sequence of approximated solutions converges to the optimal solution.<br>The two-level planning mentioned above is the same with the so-called Stackelberg Strategy, and thus the purpose of this paper is also to study an algorithm for a Stackelberg problem with plural optimization subproblems in the lower level.

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