Algebraic and geometric ideas in the theory of discrete optimization

Bibliographic Details
Main Author:	De Loera, Jesus A., 1966-
Other Authors:	Hemmecke, Raymond( 1972-), Koppe, Matthias( 1976-)
Language:	English
Published:	Philadelphia: Society for Industrial and Applied Mathematics, c2013.
Series:	MOS-SIAM series on optimization
Subjects:	Combinatorial geometry Geometry -- > Data processing Mathematical optimization -- > Data processing

Table of Contents:

1. Tools from linear and convex optimization
2. Tools from the geometry of numbers and integer optimization
3. Graver bases
4. Graver bases for block-structured integer programs
5. Introduction to generating functions
6. Decompositions of indicator functions of polyhedral
7. Barvinok's short rational generating functions
8. Global mixed-integer polynomial optimization via the summation method
9. Multicriteria integer linear optimization via Barvinok-Woods integer projection
10. Computations with polynomials
11. Grobner bases in integer programming
12. The Nullstellensatz in discrete optimization
13. Positivity of polynomials and global optimization
14. Epilogue

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