**Proceedings of Symposia in Applied Mathematics**

Volume: 61;
2004;
140 pp;
Hardcover

MSC: Primary 05; 13; 42; 52; 90;

Print ISBN: 978-0-8218-3584-5

Product Code: PSAPM/61

List Price: $46.00

Individual Member Price: $36.80

**Electronic ISBN: 978-0-8218-9276-3
Product Code: PSAPM/61.E**

List Price: $46.00

Individual Member Price: $36.80

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# Trends in Optimization

Share this page *Edited by *
*Serkan Hoşten; Jon Lee; Rekha R. Thomas*

This volume presents proceedings from the AMS short course, Trends in Optimization 2004, held at the Joint Mathematics Meetings in Phoenix (AZ). It focuses on seven exciting areas of discrete optimization.

In particular, Karen Aardal describes Lovasz's fundamental algorithm for producing a short vector in a lattice by basis reduction and H.W. Lenstra's use of this idea in the early 1980s in his polynomial-time algorithm for integer programming in fixed dimension. Aardal's article, "Lattice basis reduction in optimization: Selected Topics", is one of the most lucid presentations of the material. It also contains practical developments using computational tools.

Bernd Sturmfels' article, "Algebraic recipes for integer programming", discusses how methods of commutative algebra and algebraic combinatorics can be used successfully to attack integer programming problems. Specifically, Gröbner bases play a central role in algorithmic theory and practice. Moreover, it is shown that techniques based on short rational functions are bringing new insights, such as in computing the integer programming gap.

Overall, these articles, together with five other contributions, make this volume an impressive compilation on the state-of-the-art of optimization. It is suitable for graduate students and researchers interested in discrete optimization.

#### Table of Contents

# Table of Contents

## Trends in Optimization

- Contents v6 free
- Preface vii8 free
- Lattice basis reduction in optimization: Selected topics 112 free
- Polyhedral Methods in Discrete Optimization 2132
- Graphs and Combinatorial Optimization 3950
- Integer programming duality 6778
- The Design and Analysis of Approximation Algorithms: Facility Location as a Case Study 8596
- Algebraic Recipes for Integer Programming 99110
- Nonlinear and Semidefinite Programming 115126
- Index 139150

#### Readership

Graduate students and research mathematicians interested in discrete optimization.