Presents recent advances in the mathematical theory of discrete optimization, particularly those supported by methods from algebraic geometry, commutative algebra, convex and discrete geometry, generating functions, and other tools normally considered outside the standard curriculum in optimization.
Algebraic and Geometric Ideas in the Theory of Discrete Optimization:
- Offers several research technologies not yet well known among practitioners of discrete optimizationn
- Minimizes prerequisites for learning these methods.
- Provides a transition from linear discrete optimization to nonlinear discrete optimization.
>Offers several research technologies not yet well known among practitioners of discrete optimization, minimizes prerequisites for learning these methods, and provides a transition from linear discrete optimization to nonlinear discrete optimization.
Sprache
Verlagsort
Zielgruppe
Produkt-Hinweis
Broschur/Paperback
Klebebindung
Maße
Höhe: 247 mm
Breite: 174 mm
Dicke: 16 mm
Gewicht
ISBN-13
978-1-61197-243-6 (9781611972436)
Schweitzer Klassifikation
Jesús A. De Loera is a Professor of Mathematics and a member of the Graduate Groups in Computer Science and Applied Mathematics at University of California, Davis. His research has been recognised by an Alexander von Humboldt Fellowship, the UC Davis Chancellor Fellow award, and the 2010 INFORMS Computing Society Prize. He is an Associate Editor of SIAM Journal of Discrete Mathematics and Discrete Optimization.
List of figures; List of tables; List of algorithms; Preface; Part I. Established Tools of Discrete Optimization: 1. Tools from linear and convex optimization; 2. Tools from the geometry of numbers and integer optimization; Part II. Graver Basis Methods: 3. Graver bases; 4. Graver bases for block-structured integer programs; Part III. Generating Function Methods: 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; Part IV. Gröbner Basis Methods: 10. Computations with polynomials; 11. Gröbner bases in integer programming; Part V. Nullstellensatz and Positivstellensatz Relaxations: 12. The Nullstellensatz in discrete optimization; 13. Positivity of polynomials and global optimization; 14. Epilogue; Bibliography; Index.
