Elements of Large-Scale Mathematical Programming.

by A. M. Geoffrion

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A unifying framework of concepts central to the optimization of large structured systems is developed and used in the organization of the literature. The principal focus is on that portion of the literature concerned with developing new solution techniques for various problem structures. The basic concepts are divided in two groups (1) problem manipulations, in which a given problem is restated in an alternative form more amenable to solution, and (2) solution strategies which reduce an optimization problem to a related sequence of simpler problems that can be solved by specialized methods. By assembling elements of problem manipulation and solution strategies in various patterns, one can derive the essential aspects of most large-scale programming algorithms and even design new ones. Some of the literature is grouped according to five key patterns, and illustrative papers from each are discussed in detail. Some of the concepts presented in this study are considered in more technical detail in RM-5829. 90 pp. Bibliog.

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