Separable optimization: theory and methods
Preface to the New Edition -- Preface.-1 Preliminaries: Convex Analysis and Convex Programming -- Part I. Separable Programming -- 2 Introduction: Approximating the Separable Problem -- 3. Convex Separable Programming -- 4. Separable Programming: A Dynamic Programming Approach -- Part II. Convex Sep...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cham
Springer International Publishing
2021
Cham Imprint: Springer 2021 |
| Ausgabe: | 2nd ed. |
| Schriftenreihe: | Springer optimization and its applications
177 |
| Schlagworte: | |
| Online-Zugang: | DE-634 DE-1043 DE-92 DE-898 DE-523 DE-384 DE-19 DE-20 DE-706 DE-824 Volltext |
| Zusammenfassung: | Preface to the New Edition -- Preface.-1 Preliminaries: Convex Analysis and Convex Programming -- Part I. Separable Programming -- 2 Introduction: Approximating the Separable Problem -- 3. Convex Separable Programming -- 4. Separable Programming: A Dynamic Programming Approach -- Part II. Convex Separable Programming With Bounds on the Variables -- 5. Statement of the Main Problem. Basic Result -- 6. Version One: Linear Equality Constraints -- 7. The Algorithms -- 8. Version Two: Linear Constraint of the Form geq -- 9. Well-Posedness of Optimization Problems. On the Stability of the Set of Saddle Points of the Lagrangian -- 10. Extensions -- 11. Applications and Computational Experiments -- Part III. Selected Supplementary Topics and Applications -- 12. Applications of Convex Separable Unconstrained Nondifferentiable Optimization to Approximation Theory -- 13. About Projections in the Implementation of Stochastic Quasigradient Methods to Some Probabilistic Inventory Control Problems -- 14. Valid Inequalities, Cutting Planes and Integrality ofthe Knapsack Polytope -- 15. Relaxation of the Equality Constrained Convex Continuous Knapsack Problem -- 16. On the Solution of Multidimensional Convex Separable Continuous Knapsack Problem with Bounded Variables -- 17. Characterization of the Optimal Solution of the Convex Generalized Nonlinear Transportation Problem -- Appendices -- A. Some Definitions and Theorems from Calculus -- B. Metric, Banach and Hilbert Spaces -- C. Existence of Solutions to Optimization Problems — A General Approach -- D. Best Approximation: Existence and Uniqueness -- E. On the Solvability of a Quadratic Optimization Problem with a Feasible Region Defined as a Minkowski Sum of a Compact Set and Finitely Generated Convex Closed Cone- F. On the Cauchy-Schwarz Inequality Approach for Solving a Quadratic Optimization Problem -- G. Theorems of the Alternative -- Bibliography -- List of Notation -- List of Statements -- Index |
| Beschreibung: | 1 Online-Ressource (XVII, 356 Seiten) |
| ISBN: | 9783030784010 |
| DOI: | 10.1007/978-3-030-78401-0 |
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| edition | 2nd ed. |
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| index_date | 2024-07-03T19:05:47Z |
| indexdate | 2024-12-02T07:00:34Z |
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| isbn | 9783030784010 |
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| spelling | Stefanov, Stefan M. Verfasser aut Separable optimization theory and methods by Stefan M. Stefanov 2nd ed. Cham Springer International Publishing 2021 Cham Imprint: Springer 2021 1 Online-Ressource (XVII, 356 Seiten) txt rdacontent c rdamedia cr rdacarrier Springer optimization and its applications 177 Preface to the New Edition -- Preface.-1 Preliminaries: Convex Analysis and Convex Programming -- Part I. Separable Programming -- 2 Introduction: Approximating the Separable Problem -- 3. Convex Separable Programming -- 4. Separable Programming: A Dynamic Programming Approach -- Part II. Convex Separable Programming With Bounds on the Variables -- 5. Statement of the Main Problem. Basic Result -- 6. Version One: Linear Equality Constraints -- 7. The Algorithms -- 8. Version Two: Linear Constraint of the Form geq -- 9. Well-Posedness of Optimization Problems. On the Stability of the Set of Saddle Points of the Lagrangian -- 10. Extensions -- 11. Applications and Computational Experiments -- Part III. Selected Supplementary Topics and Applications -- 12. Applications of Convex Separable Unconstrained Nondifferentiable Optimization to Approximation Theory -- 13. About Projections in the Implementation of Stochastic Quasigradient Methods to Some Probabilistic Inventory Control Problems -- 14. Valid Inequalities, Cutting Planes and Integrality ofthe Knapsack Polytope -- 15. Relaxation of the Equality Constrained Convex Continuous Knapsack Problem -- 16. On the Solution of Multidimensional Convex Separable Continuous Knapsack Problem with Bounded Variables -- 17. Characterization of the Optimal Solution of the Convex Generalized Nonlinear Transportation Problem -- Appendices -- A. Some Definitions and Theorems from Calculus -- B. Metric, Banach and Hilbert Spaces -- C. Existence of Solutions to Optimization Problems — A General Approach -- D. Best Approximation: Existence and Uniqueness -- E. On the Solvability of a Quadratic Optimization Problem with a Feasible Region Defined as a Minkowski Sum of a Compact Set and Finitely Generated Convex Closed Cone- F. On the Cauchy-Schwarz Inequality Approach for Solving a Quadratic Optimization Problem -- G. Theorems of the Alternative -- Bibliography -- List of Notation -- List of Statements -- Index Mathematical optimization Operations research Management science Erscheint auch als Druck-Ausgabe, Hardcover 978-3-030-78400-3 Erscheint auch als Druck-Ausgabe, Softcover 978-3-030-78403-4 Springer optimization and its applications 177 (DE-604)BV039769482 177 https://doi.org/10.1007/978-3-030-78401-0 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Stefanov, Stefan M. Separable optimization theory and methods Springer optimization and its applications |
| title | Separable optimization theory and methods |
| title_auth | Separable optimization theory and methods |
| title_exact_search | Separable optimization theory and methods |
| title_exact_search_txtP | Separable optimization theory and methods |
| title_full | Separable optimization theory and methods by Stefan M. Stefanov |
| title_fullStr | Separable optimization theory and methods by Stefan M. Stefanov |
| title_full_unstemmed | Separable optimization theory and methods by Stefan M. Stefanov |
| title_short | Separable optimization |
| title_sort | separable optimization theory and methods |
| title_sub | theory and methods |
| url | https://doi.org/10.1007/978-3-030-78401-0 |
| volume_link | (DE-604)BV039769482 |
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