© 2001

Large-scale Optimization — Problems and Methods


Part of the Applied Optimization book series (APOP, volume 51)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Vladimir Tsurkov
    Pages 1-76
  3. Vladimir Tsurkov
    Pages 77-128
  4. Vladimir Tsurkov
    Pages 129-262
  5. Back Matter
    Pages 301-311

About this book


Decomposition methods aim to reduce large-scale problems to simpler problems. This monograph presents selected aspects of the dimension-reduction problem. Exact and approximate aggregations of multidimensional systems are developed and from a known model of input-output balance, aggregation methods are categorized. The issues of loss of accuracy, recovery of original variables (disaggregation), and compatibility conditions are analyzed in detail. The method of iterative aggregation in large-scale problems is studied. For fixed weights, successively simpler aggregated problems are solved and the convergence of their solution to that of the original problem is analyzed. An introduction to block integer programming is considered. Duality theory, which is widely used in continuous block programming, does not work for the integer problem. A survey of alternative methods is presented and special attention is given to combined methods of decomposition. Block problems in which the coupling variables do not enter the binding constraints are studied. These models are worthwhile because they permit a decomposition with respect to primal and dual variables by two-level algorithms instead of three-level algorithms.
Audience: This book is addressed to specialists in operations research, optimization, and optimal control.


algorithm algorithms model operations research optimal control optimization programming

Authors and affiliations

  1. 1.Computing CenterRussian Academy of SciencesMoscowRussia

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