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Optimization with Disjunctive Constraints (Paperback, Softcover reprint of the original 1st ed. 1980)
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Optimization with Disjunctive Constraints (Paperback, Softcover reprint of the original 1st ed. 1980)
Series: Lecture Notes in Economics and Mathematical Systems, 181
Expected to ship within 18 - 22 working days
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The disjunctive cut principle of Balas and Jeroslow, and the
related polyhedral annexation principle of Glover, provide new
insights into cutting plane theory. This has resulted in its
ability to not only subsume many known valid cuts but also improve
upon them. Originally a set of notes were written for the purpose
of putting together in a common terminology and framework
significant results of Glover and others using a geometric
approach, referred to in the literature as convexity cuts, and the
algebraic approach of Balas and Jeroslow known as Disjunctive cuts.
As it turned out subsequently the polyhedral annexation approach of
Glover is also closely connected with the basic disjunctive
principle of Balas and Jeroslow. In this monograph we have included
these results and have also added several published results which
seem to be of strong interest to researchers in the area of
developing strong cuts for disjunctive programs. In particular,
several results due to Balas [4,5,6,7], Glover [18,19] and Jeroslow
[23,25,26] have been used in this monograph. The appropriate
theorems are given without proof. The notes also include several
results yet to be published [32,34,35] obtained under a research
contract with the National Science Foundation to investigate
solution methods for disjunctive programs. The monograph is
self-contained and complete in the sense that it attempts to pool
together existing results which the authors viewed as important to
future research on optimization using the disjunctive cut approach.
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