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Direct method of hierarchical nonlinear optimization - reassessment after 30 years

Karbowski A.

Journal of Telecommunications and Information Technology

2004

nr 3

3-11

We consider the optimization problems which may be solved by the direct decomposition method. It is possible when the performance index is a monotone function of other performance indices, which depend on two subsets of decision variables: an individual for every inner performance index and a common one for all. Such problems may be treated as a generalization of separable problems with the additive cost and constraints functions. In the paper both the underlying theory and the basic numerical techniques are presented and compared. A special attention is paid to the guarantees of convergence in different classes of problems and to the effectiveness of calculations.