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Convexity and optimization in R [superscript n] [[electronic resource] /] / Leonard D. Berkovitz
| Convexity and optimization in R [superscript n] [[electronic resource] /] / Leonard D. Berkovitz |
| Autore | Berkovitz Leonard David <1924-> |
| Pubbl/distr/stampa | New York, : J. Wiley, c2002 |
| Descrizione fisica | 1 online resource (283 p.) |
| Disciplina |
516/.08
519.3 |
| Collana | Pure and applied mathematicss |
| Soggetto topico |
Convex sets
Mathematical optimization |
| ISBN |
1-280-36700-8
9786610367009 0-470-31182-7 0-471-46166-0 0-471-24970-X |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
CONVEXITY AND OPTIMIZATION IN R(n); CONTENTS; Preface; I Topics in Real Analysis; 1. Introduction; 2. Vectors in R(n); 3. Algebra of Sets; 4. Metric Topology of R(n); 5. Limits and Continuity; 6. Basic Property of Real Numbers; 7. Compactness; 8. Equivalent Norms and Cartesian Products; 9. Fundamental Existence Theorem; 10. Linear Transformations; 11. Differentiation in R(n); II Convex Sets in R(n); 1. Lines and Hyperplanes in R(n); 2. Properties of Convex Sets; 3. Separation Theorems; 4. Supporting Hyperplanes: Extreme Points; 5. Systems of Linear Inequalities: Theorems of the Alternative
6. Affine Geometry7. More on Separation and Support; III Convex Functions; 1. Definition and Elementary Properties; 2. Subgradients; 3. Differentiable Convex Functions; 4. Alternative Theorems for Convex Functions; 5. Application to Game Theory; IV Optimization Problems; 1. Introduction; 2. Differentiable Unconstrained Problems; 3. Optimization of Convex Functions; 4. Linear Programming Problems; 5. First-Order Conditions for Differentiable Nonlinear Programming Problems; 6. Second-Order Conditions; V Convex Programming and Duality; 1. Problem Statement 2. Necessary Conditions and Sufficient Conditions3. Perturbation Theory; 4. Lagrangian Duality; 5. Geometric Interpretation; 6. Quadratic Programming; 7. Duality in Linear Programming; VI Simplex Method; 1. Introduction; 2. Extreme Points of Feasible Set; 3. Preliminaries to Simplex Method; 4. Phase II of Simplex Method; 5. Termination and Cycling; 6. Phase I of Simplex Method; 7. Revised Simplex Method; Bibliography; Index |
| Record Nr. | UNINA-9910143190903321 |
Berkovitz Leonard David <1924->
|
||
| New York, : J. Wiley, c2002 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Convexity and optimization in R [superscript n] [[electronic resource] /] / Leonard D. Berkovitz
| Convexity and optimization in R [superscript n] [[electronic resource] /] / Leonard D. Berkovitz |
| Autore | Berkovitz Leonard David <1924-> |
| Pubbl/distr/stampa | New York, : J. Wiley, c2002 |
| Descrizione fisica | 1 online resource (283 p.) |
| Disciplina |
516/.08
519.3 |
| Collana | Pure and applied mathematicss |
| Soggetto topico |
Convex sets
Mathematical optimization |
| ISBN |
1-280-36700-8
9786610367009 0-470-31182-7 0-471-46166-0 0-471-24970-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
CONVEXITY AND OPTIMIZATION IN R(n); CONTENTS; Preface; I Topics in Real Analysis; 1. Introduction; 2. Vectors in R(n); 3. Algebra of Sets; 4. Metric Topology of R(n); 5. Limits and Continuity; 6. Basic Property of Real Numbers; 7. Compactness; 8. Equivalent Norms and Cartesian Products; 9. Fundamental Existence Theorem; 10. Linear Transformations; 11. Differentiation in R(n); II Convex Sets in R(n); 1. Lines and Hyperplanes in R(n); 2. Properties of Convex Sets; 3. Separation Theorems; 4. Supporting Hyperplanes: Extreme Points; 5. Systems of Linear Inequalities: Theorems of the Alternative
6. Affine Geometry7. More on Separation and Support; III Convex Functions; 1. Definition and Elementary Properties; 2. Subgradients; 3. Differentiable Convex Functions; 4. Alternative Theorems for Convex Functions; 5. Application to Game Theory; IV Optimization Problems; 1. Introduction; 2. Differentiable Unconstrained Problems; 3. Optimization of Convex Functions; 4. Linear Programming Problems; 5. First-Order Conditions for Differentiable Nonlinear Programming Problems; 6. Second-Order Conditions; V Convex Programming and Duality; 1. Problem Statement 2. Necessary Conditions and Sufficient Conditions3. Perturbation Theory; 4. Lagrangian Duality; 5. Geometric Interpretation; 6. Quadratic Programming; 7. Duality in Linear Programming; VI Simplex Method; 1. Introduction; 2. Extreme Points of Feasible Set; 3. Preliminaries to Simplex Method; 4. Phase II of Simplex Method; 5. Termination and Cycling; 6. Phase I of Simplex Method; 7. Revised Simplex Method; Bibliography; Index |
| Record Nr. | UNINA-9910829921703321 |
|
Berkovitz Leonard David <1924->
|
||
| New York, : J. Wiley, c2002 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Convexity and optimization in R [superscript n] / / Leonard D. Berkovitz
| Convexity and optimization in R [superscript n] / / Leonard D. Berkovitz |
| Autore | Berkovitz Leonard David <1924-> |
| Pubbl/distr/stampa | New York, : J. Wiley, c2002 |
| Descrizione fisica | 1 online resource (283 p.) |
| Disciplina | 516/.08 |
| Collana | Pure and applied mathematicss |
| Soggetto topico |
Convex sets
Mathematical optimization |
| ISBN |
1-280-36700-8
9786610367009 0-470-31182-7 0-471-46166-0 0-471-24970-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
CONVEXITY AND OPTIMIZATION IN R(n); CONTENTS; Preface; I Topics in Real Analysis; 1. Introduction; 2. Vectors in R(n); 3. Algebra of Sets; 4. Metric Topology of R(n); 5. Limits and Continuity; 6. Basic Property of Real Numbers; 7. Compactness; 8. Equivalent Norms and Cartesian Products; 9. Fundamental Existence Theorem; 10. Linear Transformations; 11. Differentiation in R(n); II Convex Sets in R(n); 1. Lines and Hyperplanes in R(n); 2. Properties of Convex Sets; 3. Separation Theorems; 4. Supporting Hyperplanes: Extreme Points; 5. Systems of Linear Inequalities: Theorems of the Alternative
6. Affine Geometry7. More on Separation and Support; III Convex Functions; 1. Definition and Elementary Properties; 2. Subgradients; 3. Differentiable Convex Functions; 4. Alternative Theorems for Convex Functions; 5. Application to Game Theory; IV Optimization Problems; 1. Introduction; 2. Differentiable Unconstrained Problems; 3. Optimization of Convex Functions; 4. Linear Programming Problems; 5. First-Order Conditions for Differentiable Nonlinear Programming Problems; 6. Second-Order Conditions; V Convex Programming and Duality; 1. Problem Statement 2. Necessary Conditions and Sufficient Conditions3. Perturbation Theory; 4. Lagrangian Duality; 5. Geometric Interpretation; 6. Quadratic Programming; 7. Duality in Linear Programming; VI Simplex Method; 1. Introduction; 2. Extreme Points of Feasible Set; 3. Preliminaries to Simplex Method; 4. Phase II of Simplex Method; 5. Termination and Cycling; 6. Phase I of Simplex Method; 7. Revised Simplex Method; Bibliography; Index |
| Record Nr. | UNINA-9910876604903321 |
|
Berkovitz Leonard David <1924->
|
||
| New York, : J. Wiley, c2002 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||