Nonlinear Discrete Optimization An Algorithmic Theory |
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| Author:
| Onn, Shmuel |
| Series title: | Zurich Lectures in Advanced Mathematics Ser. |
| ISBN: | 978-3-03719-093-7 |
| Publication Date: | Sep 2010 |
| Publisher: | European Mathematical Society
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| Book Format: | Paperback |
| List Price: | USD $42.00 |
Book Description:
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This monograph develops an algorithmic theory of nonlinear discrete optimization. It introduces a simple and useful setup, which enables the polynomial time solution of broad fundamental classes of nonlinear combinatorial optimization and integer programming problems in variable dimension. An important part of this theory is enhanced by recent developments in the algebra of Graver bases. The power of the theory is demonstrated by deriving the first polynomial time algorithms in a...
More DescriptionThis monograph develops an algorithmic theory of nonlinear discrete optimization. It introduces a simple and useful setup, which enables the polynomial time solution of broad fundamental classes of nonlinear combinatorial optimization and integer programming problems in variable dimension. An important part of this theory is enhanced by recent developments in the algebra of Graver bases. The power of the theory is demonstrated by deriving the first polynomial time algorithms in a variety of application areas within operations research and statistics, including vector partitioning, matroid optimization, experimental design, multicommodity flows, multi-index transportation and privacy in statistical databases. This monograph is intended for graduate students and researchers. It is accessible to anyone with standard undergraduate knowledge and mathematical maturity.