Mathematical programming [[electronic resource] ] : theory and methods / / S. M. Sinha

• Record Nr.: UNINA9910458230703321
• Autore: Sinha S. M
• Pubbl/distr/stampa: New Delhi, : Elsevier, 2006
• ISBN: 1-281-31134-0; 9786611311346; 0-08-053593-3
• Edizione: [1st ed.]
• Descrizione fisica: 1 online resource (589 p.)
• Disciplina: 005.1/15
• Soggetti: Programming (Mathematics); Mathematics; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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; Chapter 14. The Revised Simplex Method
• Sommario/riassunto: Mathematical Programming, a branch of Operations Research, is perhaps the most efficient technique in making optimal decisions. It has a very wide application in the analysis of management problems, in business and industry, in economic studies, in military problems and in many other fields of our present day activities. In this keen competetive world, the problems are getting more and more complicated ahnd efforts are being made to deal with these challenging problems. This book presents from the origin to the recent developments in mathematical programming. The book has wide coverage and