Computational methods for optimizing distributed systems /:
Computational methods for optimizing distributed systems.
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Orlando :
Academic Press,
1984.
|
| Series: | Mathematics in science and engineering ;
v. 173. |
| Subjects: | |
| Online Access: | DE-862 DE-863 DE-862 DE-863 |
| Summary: | Computational methods for optimizing distributed systems. |
| Physical Description: | 1 online resource (xiii, 317 pages) |
| Bibliography: | Includes bibliographical references (pages 301-312) and index. |
| ISBN: | 9780126854800 0126854807 9780080956787 0080956785 |
Staff View
MARC
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| 490 | 1 | |a Mathematics in science and engineering ; |v v. 173 | |
| 504 | |a Includes bibliographical references (pages 301-312) and index. | ||
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| 505 | 0 | |a Front Cover; Computational Methods for Optimizing Distributed Systems; Copyright Page; Contents; Preface; Chapter I. Mathematical Background; 1. Introduction; 2. Some Basic Concepts in Functional Analysis; 3. Some Basic Concepts in Measure Theory; 4. Some Function Spaces; 5. Relaxed Controls; 6. Multivalued Functions; 7. Bibliographical Remarks; Chapter II. Boundary Value Problems of Parabolic Type; 1. Introduction; 2. Boundary-Value Problems-Basic Definitions and Assumptions; 3. Three Elementary Lemmas; 4. A Priori Estimates; 5. Existence and Uniqueness of Solutions; 6. A Continuity Property | |
| 505 | 8 | |a 7. Certain Properties of Solutions of Equation (2.1)8. Boundary-Value Problems in General Form; 9. A Maximum Principle; Chapter III. Optimal Control of First Boundary Problems: Strong Variation Techniques; 1. Introduction; 2. System Description; 3. The Optimal Control Problems; 4. The Hamiltonian Functions; 5. The Successive Controls; 6. The Algorithm; 7. Necessary and Sufficient Conditions for Optimality; 8. Numerical Consideration; 9. Examples; 10. Discussion; Chapter IV. Optimal Policy of First Boundary Problems: Gradient Techniques; 1. Introduction; 2. System Description | |
| 505 | 8 | |a 3. The Optimization Problem4. An Increment Formula; 5. The Gradient of the Cost Functional; 6. A Conditional Gradient Algorithm; 7. Numerical Consideration and an Examples; 8. Optimal Control Problems with Terminal Inequality Constraints; 9. The Finite Element Method; 10. Discussion; Chapter V. Relaxed Controls and the Convergence of Optimal Control Algorithms; 1. Introduction; 2. The Strong Variational Algorithm; 3. The Conditional Gradient Algorithm; 4. The Feasible Directions Algorithm; 5. Discussion; Chapter VI. Optimal Control Problems Involving Second Boundary-Value Problems | |
| 505 | 8 | |a 1. Introduction2. The General Problem Statement; 3. Preparatory Results; 4. A Basic Inequality; 5. An Optimal Control Problem with a Linear Cost Functional; 6. An Optimal Control Problem with a Linear System; 7. The Finite Element Method; 8. Discussion; Appendix I: Stochastic Optimal Control Problems; Appendix II: Certain Results on Partial Differential Equations Needed in Chapters III, IV, and V; Appendix III: An Algorithm of Quadratic Programming; Appendix IV: A Quasi-Newton Method for Nonlinear Function Minimization with Linear Constraints | |
| 505 | 8 | |a Appendix V: An Algorithm for Optimal Control Problems of Linear Lumped Parameter SystemsAppendix VI: Meyer-Polak Proximity Algorithm; References; List of Notation; Index | |
| 520 | |a Computational methods for optimizing distributed systems. | ||
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| 650 | 0 | |a Boundary value problems |x Numerical solutions. |0 http://id.loc.gov/authorities/subjects/sh85016105 | |
| 650 | 0 | |a Distributed parameter systems. |0 http://id.loc.gov/authorities/subjects/sh85038542 | |
| 650 | 6 | |a Équations différentielles paraboliques |x Solutions numériques. | |
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| author | Teo, K. L. |
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| contents | Front Cover; Computational Methods for Optimizing Distributed Systems; Copyright Page; Contents; Preface; Chapter I. Mathematical Background; 1. Introduction; 2. Some Basic Concepts in Functional Analysis; 3. Some Basic Concepts in Measure Theory; 4. Some Function Spaces; 5. Relaxed Controls; 6. Multivalued Functions; 7. Bibliographical Remarks; Chapter II. Boundary Value Problems of Parabolic Type; 1. Introduction; 2. Boundary-Value Problems-Basic Definitions and Assumptions; 3. Three Elementary Lemmas; 4. A Priori Estimates; 5. Existence and Uniqueness of Solutions; 6. A Continuity Property 7. Certain Properties of Solutions of Equation (2.1)8. Boundary-Value Problems in General Form; 9. A Maximum Principle; Chapter III. Optimal Control of First Boundary Problems: Strong Variation Techniques; 1. Introduction; 2. System Description; 3. The Optimal Control Problems; 4. The Hamiltonian Functions; 5. The Successive Controls; 6. The Algorithm; 7. Necessary and Sufficient Conditions for Optimality; 8. Numerical Consideration; 9. Examples; 10. Discussion; Chapter IV. Optimal Policy of First Boundary Problems: Gradient Techniques; 1. Introduction; 2. System Description 3. The Optimization Problem4. An Increment Formula; 5. The Gradient of the Cost Functional; 6. A Conditional Gradient Algorithm; 7. Numerical Consideration and an Examples; 8. Optimal Control Problems with Terminal Inequality Constraints; 9. The Finite Element Method; 10. Discussion; Chapter V. Relaxed Controls and the Convergence of Optimal Control Algorithms; 1. Introduction; 2. The Strong Variational Algorithm; 3. The Conditional Gradient Algorithm; 4. The Feasible Directions Algorithm; 5. Discussion; Chapter VI. Optimal Control Problems Involving Second Boundary-Value Problems 1. Introduction2. The General Problem Statement; 3. Preparatory Results; 4. A Basic Inequality; 5. An Optimal Control Problem with a Linear Cost Functional; 6. An Optimal Control Problem with a Linear System; 7. The Finite Element Method; 8. Discussion; Appendix I: Stochastic Optimal Control Problems; Appendix II: Certain Results on Partial Differential Equations Needed in Chapters III, IV, and V; Appendix III: An Algorithm of Quadratic Programming; Appendix IV: A Quasi-Newton Method for Nonlinear Function Minimization with Linear Constraints Appendix V: An Algorithm for Optimal Control Problems of Linear Lumped Parameter SystemsAppendix VI: Meyer-Polak Proximity Algorithm; References; List of Notation; Index |
| ctrlnum | (OCoLC)316568414 |
| dewey-full | 515.3/53 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.3/53 |
| dewey-search | 515.3/53 |
| dewey-sort | 3515.3 253 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn316568414 |
| illustrated | Not Illustrated |
| indexdate | 2025-04-11T08:36:20Z |
| institution | BVB |
| isbn | 9780126854800 0126854807 9780080956787 0080956785 |
| language | English |
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| series | Mathematics in science and engineering ; |
| series2 | Mathematics in science and engineering ; |
| spelling | Teo, K. L. http://id.loc.gov/authorities/names/n81051843 Computational methods for optimizing distributed systems / K.L. Teo, Z.S. Wu. Orlando : Academic Press, 1984. 1 online resource (xiii, 317 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Mathematics in science and engineering ; v. 173 Includes bibliographical references (pages 301-312) and index. Print version record. Front Cover; Computational Methods for Optimizing Distributed Systems; Copyright Page; Contents; Preface; Chapter I. Mathematical Background; 1. Introduction; 2. Some Basic Concepts in Functional Analysis; 3. Some Basic Concepts in Measure Theory; 4. Some Function Spaces; 5. Relaxed Controls; 6. Multivalued Functions; 7. Bibliographical Remarks; Chapter II. Boundary Value Problems of Parabolic Type; 1. Introduction; 2. Boundary-Value Problems-Basic Definitions and Assumptions; 3. Three Elementary Lemmas; 4. A Priori Estimates; 5. Existence and Uniqueness of Solutions; 6. A Continuity Property 7. Certain Properties of Solutions of Equation (2.1)8. Boundary-Value Problems in General Form; 9. A Maximum Principle; Chapter III. Optimal Control of First Boundary Problems: Strong Variation Techniques; 1. Introduction; 2. System Description; 3. The Optimal Control Problems; 4. The Hamiltonian Functions; 5. The Successive Controls; 6. The Algorithm; 7. Necessary and Sufficient Conditions for Optimality; 8. Numerical Consideration; 9. Examples; 10. Discussion; Chapter IV. Optimal Policy of First Boundary Problems: Gradient Techniques; 1. Introduction; 2. System Description 3. The Optimization Problem4. An Increment Formula; 5. The Gradient of the Cost Functional; 6. A Conditional Gradient Algorithm; 7. Numerical Consideration and an Examples; 8. Optimal Control Problems with Terminal Inequality Constraints; 9. The Finite Element Method; 10. Discussion; Chapter V. Relaxed Controls and the Convergence of Optimal Control Algorithms; 1. Introduction; 2. The Strong Variational Algorithm; 3. The Conditional Gradient Algorithm; 4. The Feasible Directions Algorithm; 5. Discussion; Chapter VI. Optimal Control Problems Involving Second Boundary-Value Problems 1. Introduction2. The General Problem Statement; 3. Preparatory Results; 4. A Basic Inequality; 5. An Optimal Control Problem with a Linear Cost Functional; 6. An Optimal Control Problem with a Linear System; 7. The Finite Element Method; 8. Discussion; Appendix I: Stochastic Optimal Control Problems; Appendix II: Certain Results on Partial Differential Equations Needed in Chapters III, IV, and V; Appendix III: An Algorithm of Quadratic Programming; Appendix IV: A Quasi-Newton Method for Nonlinear Function Minimization with Linear Constraints Appendix V: An Algorithm for Optimal Control Problems of Linear Lumped Parameter SystemsAppendix VI: Meyer-Polak Proximity Algorithm; References; List of Notation; Index Computational methods for optimizing distributed systems. Differential equations, Parabolic Numerical solutions. http://id.loc.gov/authorities/subjects/sh85037911 Boundary value problems Numerical solutions. http://id.loc.gov/authorities/subjects/sh85016105 Distributed parameter systems. http://id.loc.gov/authorities/subjects/sh85038542 Équations différentielles paraboliques Solutions numériques. Problèmes aux limites Solutions numériques. Systèmes à paramètres répartis. MATHEMATICS Differential Equations Partial. bisacsh Boundary value problems Numerical solutions fast Differential equations, Parabolic Numerical solutions fast Distributed parameter systems fast Wu, Z. S. http://id.loc.gov/authorities/names/n83176947 Print version: Teo, K.L. Computational methods for optimizing distributed systems. Orlando : Academic Press, 1984 9780126854800 (DLC) 83015737 (OCoLC)10018031 Mathematics in science and engineering ; v. 173. http://id.loc.gov/authorities/names/n42015986 |
| spellingShingle | Teo, K. L. Computational methods for optimizing distributed systems / Mathematics in science and engineering ; Front Cover; Computational Methods for Optimizing Distributed Systems; Copyright Page; Contents; Preface; Chapter I. Mathematical Background; 1. Introduction; 2. Some Basic Concepts in Functional Analysis; 3. Some Basic Concepts in Measure Theory; 4. Some Function Spaces; 5. Relaxed Controls; 6. Multivalued Functions; 7. Bibliographical Remarks; Chapter II. Boundary Value Problems of Parabolic Type; 1. Introduction; 2. Boundary-Value Problems-Basic Definitions and Assumptions; 3. Three Elementary Lemmas; 4. A Priori Estimates; 5. Existence and Uniqueness of Solutions; 6. A Continuity Property 7. Certain Properties of Solutions of Equation (2.1)8. Boundary-Value Problems in General Form; 9. A Maximum Principle; Chapter III. Optimal Control of First Boundary Problems: Strong Variation Techniques; 1. Introduction; 2. System Description; 3. The Optimal Control Problems; 4. The Hamiltonian Functions; 5. The Successive Controls; 6. The Algorithm; 7. Necessary and Sufficient Conditions for Optimality; 8. Numerical Consideration; 9. Examples; 10. Discussion; Chapter IV. Optimal Policy of First Boundary Problems: Gradient Techniques; 1. Introduction; 2. System Description 3. The Optimization Problem4. An Increment Formula; 5. The Gradient of the Cost Functional; 6. A Conditional Gradient Algorithm; 7. Numerical Consideration and an Examples; 8. Optimal Control Problems with Terminal Inequality Constraints; 9. The Finite Element Method; 10. Discussion; Chapter V. Relaxed Controls and the Convergence of Optimal Control Algorithms; 1. Introduction; 2. The Strong Variational Algorithm; 3. The Conditional Gradient Algorithm; 4. The Feasible Directions Algorithm; 5. Discussion; Chapter VI. Optimal Control Problems Involving Second Boundary-Value Problems 1. Introduction2. The General Problem Statement; 3. Preparatory Results; 4. A Basic Inequality; 5. An Optimal Control Problem with a Linear Cost Functional; 6. An Optimal Control Problem with a Linear System; 7. The Finite Element Method; 8. Discussion; Appendix I: Stochastic Optimal Control Problems; Appendix II: Certain Results on Partial Differential Equations Needed in Chapters III, IV, and V; Appendix III: An Algorithm of Quadratic Programming; Appendix IV: A Quasi-Newton Method for Nonlinear Function Minimization with Linear Constraints Appendix V: An Algorithm for Optimal Control Problems of Linear Lumped Parameter SystemsAppendix VI: Meyer-Polak Proximity Algorithm; References; List of Notation; Index Differential equations, Parabolic Numerical solutions. http://id.loc.gov/authorities/subjects/sh85037911 Boundary value problems Numerical solutions. http://id.loc.gov/authorities/subjects/sh85016105 Distributed parameter systems. http://id.loc.gov/authorities/subjects/sh85038542 Équations différentielles paraboliques Solutions numériques. Problèmes aux limites Solutions numériques. Systèmes à paramètres répartis. MATHEMATICS Differential Equations Partial. bisacsh Boundary value problems Numerical solutions fast Differential equations, Parabolic Numerical solutions fast Distributed parameter systems fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85037911 http://id.loc.gov/authorities/subjects/sh85016105 http://id.loc.gov/authorities/subjects/sh85038542 |
| title | Computational methods for optimizing distributed systems / |
| title_auth | Computational methods for optimizing distributed systems / |
| title_exact_search | Computational methods for optimizing distributed systems / |
| title_full | Computational methods for optimizing distributed systems / K.L. Teo, Z.S. Wu. |
| title_fullStr | Computational methods for optimizing distributed systems / K.L. Teo, Z.S. Wu. |
| title_full_unstemmed | Computational methods for optimizing distributed systems / K.L. Teo, Z.S. Wu. |
| title_short | Computational methods for optimizing distributed systems / |
| title_sort | computational methods for optimizing distributed systems |
| topic | Differential equations, Parabolic Numerical solutions. http://id.loc.gov/authorities/subjects/sh85037911 Boundary value problems Numerical solutions. http://id.loc.gov/authorities/subjects/sh85016105 Distributed parameter systems. http://id.loc.gov/authorities/subjects/sh85038542 Équations différentielles paraboliques Solutions numériques. Problèmes aux limites Solutions numériques. Systèmes à paramètres répartis. MATHEMATICS Differential Equations Partial. bisacsh Boundary value problems Numerical solutions fast Differential equations, Parabolic Numerical solutions fast Distributed parameter systems fast |
| topic_facet | Differential equations, Parabolic Numerical solutions. Boundary value problems Numerical solutions. Distributed parameter systems. Équations différentielles paraboliques Solutions numériques. Problèmes aux limites Solutions numériques. Systèmes à paramètres répartis. MATHEMATICS Differential Equations Partial. Boundary value problems Numerical solutions Differential equations, Parabolic Numerical solutions Distributed parameter systems |
| work_keys_str_mv | AT teokl computationalmethodsforoptimizingdistributedsystems AT wuzs computationalmethodsforoptimizingdistributedsystems |