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Appendix. The Main Approaches in Hierarchical Optimization

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Hierarchical Optimization and Mathematical Physics

Part of the book series: Applied Optimization ((APOP,volume 37))

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Abstract

Below, we present the main types of optimization problems with block constraint structure. We describe the Dantzig-Wolfe decomposition. This approach is fairly well covered in the literature, therefore, we present it briefly here, just to introduce the main ideas. The Kornai-Liptak decomposition principle is presented more comprehensively. Along with the main published constructions, we consider various schemes of reducing dimension based on the iterative resource redistribution. Special attention is given to the method of parametric decomposition, which is the standard method for optimizing large-scale systems and generalizes many well-known decomposition approaches. Here, the foundations of iterative aggregation are described. This method was initially applied in particular economic models. However, it was later modified and generalized for a wide class of problems of hierarchical optimization. Finally, the use of the Lagrange functional for the organization of the two-level iterative process with respect to primal and dual variables allows us to formulate a fairly universal approach to reducing dimensions in block problems of optimal control.

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  1. Computing Center, Russian Academy of Sciences, Moscow, Russia

    Vladimir Tsurkov

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  1. Vladimir Tsurkov
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Tsurkov, V. (2000). Appendix. The Main Approaches in Hierarchical Optimization. In: Hierarchical Optimization and Mathematical Physics. Applied Optimization, vol 37. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4667-2_5

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  • DOI: https://doi.org/10.1007/978-1-4615-4667-2_5

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