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Mathematical Programming : Theory and Methods.
Mathematical Programming, a branch of Operations Research, is perhaps the most efficient technique in making optimal decisions. This self-contained book is an overview of mathematical programming from its origins. It is suitable both as a text and as a reference.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Burlington :
Elsevier,
2006.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Mathematical Programming: Theory and Methods; Copyright Page; Contents; Chapter 1. Introduction; 1.1 Background and Historical Sketch; 1.2. Linear Programming; 1.3. Illustrative Examples; 1.4. Graphical Solutions; 1.5. Nonlinear Programming; PART 1: MATHEMATICAL FOUNDATIONS; Chapter 2. Basic Theory of Sets and Functions; 2.1. Sets; 2.2. Vectors; 2.3. Topological Properties of Rn; 2.4. Sequences and Subsequences; 2.5. Mappings and Functions; 2.6. Continuous Functions; 2.7. Infimum and Supremum of Functions; 2.8. Minima and Maxima of Functions; 2.9. Differentiable Functions
- Chapter 3. Vector Spaces3.1. Fields; 3.2. Vector Spaces; 3.3. Subspaces; 3.4. Linear Dependence; 3.5. Basis and Dimension; 3.6. Inner Product Spaces; Chapter 4. Matrices and Determinants; 4.1. Matrices; 4.2. Relations and Operations; 4.3. Partitioning of Matrices; 4.4. Rank of a Matrix; 4.5. Determinants; 4.6. Properties of Determinants; 4.7. Minors and Cofactors; 4.8. Determinants and Rank; 4.9. The Inverse Matrix; Chapter 5. Linear Transformations and Rank; 5.1. Linear Transformations and Rank; 5.2. Product of Linear Transformations; 5.3. Elementary Transformations
- 5.4. Echelon Matrices and RankChapter 6. Quadratic Forms and Eigenvalue Problems; 6.1. Quadratic Forms; 6.2. Definite Quadratic Forms; 6.3. Characteristic Vectors and Characteristic Values; Chapter 7. Systems of Linear Equations and Linear Inequalities; 7.1. Linear Equations; 7.2. Existence Theorems for Systems of Linear Equations; 7.3. Basic Solutions and Degeneracy; 7.4. Theorems of the Alternative; Chapter 8. Convex Sets and Convex Cones; 8.1. Introduction and Preliminary Definitions; 8.2. Convex Sets and their Properties; 8.3. Convex Hulls; 8.4. Separation and Support of Convex Sets
- 8.5. Convex Polytopes and Polyhedra8.6. Convex Cones; Chapter 9. Convex and Concave Functions; 9.1. Definitions and Basic Properties; 9.2. Differentiable Convex Functions; 9.3. Generalization of Convex Functions; 9.4. Exercises; PART 2: LINEAR PROGRAMMING; Chapter 10. Linear Programming Problems; 10.1. The General Problem; 10.2. Equivalent Formulations; 10.3. Definitions and Terminologies; 10.4. Basic Solutions of Linear Programs; 10.5. Fundamental Properties of Linear Programs; 10.6. Exercises; Chapter 11. Simplex Method: Theory and Computation; 11.1. Introduction
- 11.2. Theory of the Simplex Method11.3. Method of Computation: The Simplex Algorithm; 11.4. The Simplex Tableau; 11.5. Replacement Operation; 11.6. Example; 11.7. Exercises; Chapter 12. Simplex Method: Initial Basic Feasible Solution; 12.1. Introduction: Artificial Variable Techniques; 12.2. The Two-Phase Method [117]; 12.3. Examples; 12.4. The Method of Penalties [71]; 12.5. Examples: Penalty Method; 12.6. Inconsistency and Redundancy; 12.7. Exercises; Chapter 13. Degeneracy in Linear Programming; 13.1. Introduction; 13.2. Charnes' Perturbation Method; 13.3. Example; 13.4. Exercises