Algebraic and Geometric Ideas in the Theory of 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.