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Nonlinear Discrete Optimization: An Algorithmic Theory
Shmuel Onn, Israel Institute of Technology, Haifa, Israel
A publication of the European Mathematical Society.
cover
Zurich Lectures in Advanced Mathematics
2010; 147 pp; softcover
Volume: 13
ISBN-10: 3-03719-093-0
ISBN-13: 978-3-03719-093-7
List Price: US$42
Member Price: US$33.60
Order Code: EMSZLEC/13
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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 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.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

Readership

Graduate students and research mathematicians interested in nonlinear discrete optimization.

Table of Contents

  • Introduction
  • Convex discrete maximization
  • Nonlinear integer programming
  • \(n\)-Fold integer programming
  • Multiway tables and universality
  • Nonlinear combinatorial optimization
  • Bibliography
  • Index
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