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Applied Optimization Vol 83 - Aggregation in Large-Scale Optimization (Springer, 2003) pdf

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Description

 							
  
  ISBN
9781461348122
  
  When analyzing systems with a large number of parameters, the dimen­ 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 orig­ 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, at·
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. 						

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