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AuthorLitvinchev, Igor. author
TitleAggregation in Large-Scale Optimization [electronic resource] / by Igor Litvinchev, Vladimir Tsurkov
ImprintBoston, MA : Springer US : Imprint: Springer, 2003
Connect tohttp://dx.doi.org/10.1007/978-1-4419-9154-6
Descript XII, 291 p. online resource

SUMMARY

When analyzing systems with a large number of parameters, the dimenยญ sion of the original system may present insurmountable difficulties for the analysis. It may then be convenient to reformulate the original system in terms of substantially fewer aggregated variables, or macrovariables. In other words, an original system with an n-dimensional vector of states is reformulated as a system with a vector of dimension much less than n. The aggregated variables are either readily defined and processed, or the aggregated system may be considered as an approximate model for the origยญ inal system. In the latter case, the operation of the original system can be exhaustively analyzed within the framework of the aggregated model, and one faces the problems of defining the rules for introducing macrovariables, specifying loss of information and accuracy, recovering original variables from aggregates, etc. We consider also in detail the so-called iterative aggregation approach. It constructs an iterative process, atยท every step of which a macroproblem is solved that is simpler than the original problem because of its lower dimension. Aggregation weights are then updated, and the procedure passes to the next step. Macrovariables are commonly used in coordinating problems of hierarchical optimization


Mathematics System theory Mathematical models Mathematical optimization Calculus of variations Mathematics Optimization Calculus of Variations and Optimal Control; Optimization Systems Theory Control Mathematical Modeling and Industrial Mathematics



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