Aggregation in Large-Scale Optimization

  • Igor Litvinchev
  • Vladimir Tsurkov

Part of the Applied Optimization book series (APOP, volume 83)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Igor Litvinchev, Vladimir Tsurkov
    Pages 1-60
  3. Igor Litvinchev, Vladimir Tsurkov
    Pages 61-161
  4. Igor Litvinchev, Vladimir Tsurkov
    Pages 163-287
  5. Back Matter
    Pages 289-291

About this book

Introduction

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.

Keywords

Optimal control operations research optimization

Authors and affiliations

  • Igor Litvinchev
    • 1
  • Vladimir Tsurkov
    • 1
  1. 1.Computing CenterRussian Academy of SciencesMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-9154-6
  • Copyright Information Springer-Verlag US 2003
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-4812-2
  • Online ISBN 978-1-4419-9154-6
  • Series Print ISSN 1384-6485
  • About this book