Zurich Lectures in Advanced Mathematics 2010; 147 pp; softcover Volume: 13 ISBN10: 3037190930 ISBN13: 9783037190937 List Price: US$42 Member Price: US$33.60 Order Code: EMSZLEC/13
 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, multiindex 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
