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