Proceedings of Symposia in Applied Mathematics 2004; 140 pp; hardcover Volume: 61 ISBN10: 082183584X ISBN13: 9780821835845 List Price: US$46 Member Price: US$36.80 Order Code: PSAPM/61
 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 polynomialtime 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 stateoftheart of optimization. It is suitable for graduate students and researchers interested in discrete optimization. Readership Graduate students and research mathematicians interested in discrete optimization. Table of Contents  K. Aardal  Lattice basis reduction in optimization: Selected topics
 A. Atamtürk  Polyhedral methods in discrete optimization
 G. Cornuéjols  Graphs and combinatorial optimization
 J. B. Lasserre  Integer programming duality
 D. B. Shmoys  The design and analysis of approximation algorithms: Facility location as a case study
 B. Sturmfels  Algebraic recipes for integer programming
 S. J. Wright  Nonlinear and semidefinite programming
 Index
