# Nonlinear Discrete Optimization: An Algorithmic Theory

Share this page
*Shmuel Onn*

A publication of the European Mathematical Society

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.