Optimization :: a theory of necessary conditions /
This book presents a comprehensive treatment of necessary conditions for general optimization problems. The presentation is carried out in the context of a general theory for extremal problems in a topological vector space setting. Following a brief summary of the required background, generalized La...
Gespeichert in:
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, New Jersey :
Princeton University Press,
1976.
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| Schriftenreihe: | Princeton legacy library.
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| Zusammenfassung: | This book presents a comprehensive treatment of necessary conditions for general optimization problems. The presentation is carried out in the context of a general theory for extremal problems in a topological vector space setting. Following a brief summary of the required background, generalized Lagrange multiplier rules are derived for optimization problems with equality and generalized "inequality" constraints. The treatment stresses the importance of the choice of the underlying set over which the optimization is to be performed, the delicate balance between differentiability-continuity requirements on the constraint functionals, and the manner in which the underlying set is approximated by a convex set. The generalized multiplier rules are used to derive abstract maximum principles for classes of optimization problems defined in terms of operator equations in a Banach space. It is shown that special cases include the usual maximum principles for general optimal control problems described in terms of diverse systems such as ordinary differential equations, functional differential equations, Volterra integral equations, and difference equations. Careful distinction is made throughout the analysis between "local" and "global" maximum principles.Originally published in 1977.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. |
| Beschreibung: | 1 online resource (440 pages) |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781400870530 1400870534 0691081417 9780691081410 |
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| 505 | 0 | 0 | |t Frontmatter -- |t CONTENTS -- |t PREFACE -- |t SUMMARY OF NOTATION -- |t CHAPTER I. Mathematical Preliminaries -- |t CHAPTER II. A Basic Optimization Problem in Simplified Form -- |t CHAPTER III. A General Multiplier Rule -- |t CHAPTER IV. Optimization with Operator Equation Restrictions -- |t CHAPTER V. Optimal Control Problems with Ordinary Differential Equation Constraints -- |t CHAPTER VI. Optimal Control Problems with Parameters and Related Problems -- |t CHAPTER VII. Miscellaneous Optimal Control Problems -- |t APPENDIX. Volterra-Type Operators -- |t NOTES AND HISTORICAL COMMENTS -- |t REFERENCES -- |t SUBJECT INDEX -- |t Backmatter |
| 520 | |a This book presents a comprehensive treatment of necessary conditions for general optimization problems. The presentation is carried out in the context of a general theory for extremal problems in a topological vector space setting. Following a brief summary of the required background, generalized Lagrange multiplier rules are derived for optimization problems with equality and generalized "inequality" constraints. The treatment stresses the importance of the choice of the underlying set over which the optimization is to be performed, the delicate balance between differentiability-continuity requirements on the constraint functionals, and the manner in which the underlying set is approximated by a convex set. The generalized multiplier rules are used to derive abstract maximum principles for classes of optimization problems defined in terms of operator equations in a Banach space. It is shown that special cases include the usual maximum principles for general optimal control problems described in terms of diverse systems such as ordinary differential equations, functional differential equations, Volterra integral equations, and difference equations. Careful distinction is made throughout the analysis between "local" and "global" maximum principles.Originally published in 1977.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. | ||
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| contents | Frontmatter -- CONTENTS -- PREFACE -- SUMMARY OF NOTATION -- CHAPTER I. Mathematical Preliminaries -- CHAPTER II. A Basic Optimization Problem in Simplified Form -- CHAPTER III. A General Multiplier Rule -- CHAPTER IV. Optimization with Operator Equation Restrictions -- CHAPTER V. Optimal Control Problems with Ordinary Differential Equation Constraints -- CHAPTER VI. Optimal Control Problems with Parameters and Related Problems -- CHAPTER VII. Miscellaneous Optimal Control Problems -- APPENDIX. Volterra-Type Operators -- NOTES AND HISTORICAL COMMENTS -- REFERENCES -- SUBJECT INDEX -- Backmatter |
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| discipline | Mathematik |
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| spelling | Neustadt, Lucien W., author. Optimization : a theory of necessary conditions / Lucien W. Neustadt. Princeton, New Jersey : Princeton University Press, 1976. ©1976 1 online resource (440 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier data file Princeton Legacy Library Includes bibliographical references and index. Print version record. Frontmatter -- CONTENTS -- PREFACE -- SUMMARY OF NOTATION -- CHAPTER I. Mathematical Preliminaries -- CHAPTER II. A Basic Optimization Problem in Simplified Form -- CHAPTER III. A General Multiplier Rule -- CHAPTER IV. Optimization with Operator Equation Restrictions -- CHAPTER V. Optimal Control Problems with Ordinary Differential Equation Constraints -- CHAPTER VI. Optimal Control Problems with Parameters and Related Problems -- CHAPTER VII. Miscellaneous Optimal Control Problems -- APPENDIX. Volterra-Type Operators -- NOTES AND HISTORICAL COMMENTS -- REFERENCES -- SUBJECT INDEX -- Backmatter This book presents a comprehensive treatment of necessary conditions for general optimization problems. The presentation is carried out in the context of a general theory for extremal problems in a topological vector space setting. Following a brief summary of the required background, generalized Lagrange multiplier rules are derived for optimization problems with equality and generalized "inequality" constraints. The treatment stresses the importance of the choice of the underlying set over which the optimization is to be performed, the delicate balance between differentiability-continuity requirements on the constraint functionals, and the manner in which the underlying set is approximated by a convex set. The generalized multiplier rules are used to derive abstract maximum principles for classes of optimization problems defined in terms of operator equations in a Banach space. It is shown that special cases include the usual maximum principles for general optimal control problems described in terms of diverse systems such as ordinary differential equations, functional differential equations, Volterra integral equations, and difference equations. Careful distinction is made throughout the analysis between "local" and "global" maximum principles.Originally published in 1977.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. Mathematical optimization. http://id.loc.gov/authorities/subjects/sh85082127 Optimisation mathématique. MATHEMATICS General. bisacsh MATHEMATICS Topology. bisacsh Mathematical optimization fast Print version: Neustadt, Lucien W. Optimization : a theory of necessary conditions. Princeton, New Jersey : Princeton University Press, ©1976 xi, 424 pages Princeton legacy library. 9780691616834 Princeton legacy library. http://id.loc.gov/authorities/names/no2014116408 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=946930 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=946930 Volltext |
| spellingShingle | Neustadt, Lucien W. Optimization : a theory of necessary conditions / Princeton legacy library. Frontmatter -- CONTENTS -- PREFACE -- SUMMARY OF NOTATION -- CHAPTER I. Mathematical Preliminaries -- CHAPTER II. A Basic Optimization Problem in Simplified Form -- CHAPTER III. A General Multiplier Rule -- CHAPTER IV. Optimization with Operator Equation Restrictions -- CHAPTER V. Optimal Control Problems with Ordinary Differential Equation Constraints -- CHAPTER VI. Optimal Control Problems with Parameters and Related Problems -- CHAPTER VII. Miscellaneous Optimal Control Problems -- APPENDIX. Volterra-Type Operators -- NOTES AND HISTORICAL COMMENTS -- REFERENCES -- SUBJECT INDEX -- Backmatter Mathematical optimization. http://id.loc.gov/authorities/subjects/sh85082127 Optimisation mathématique. MATHEMATICS General. bisacsh MATHEMATICS Topology. bisacsh Mathematical optimization fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85082127 |
| title | Optimization : a theory of necessary conditions / |
| title_alt | Frontmatter -- CONTENTS -- PREFACE -- SUMMARY OF NOTATION -- CHAPTER I. Mathematical Preliminaries -- CHAPTER II. A Basic Optimization Problem in Simplified Form -- CHAPTER III. A General Multiplier Rule -- CHAPTER IV. Optimization with Operator Equation Restrictions -- CHAPTER V. Optimal Control Problems with Ordinary Differential Equation Constraints -- CHAPTER VI. Optimal Control Problems with Parameters and Related Problems -- CHAPTER VII. Miscellaneous Optimal Control Problems -- APPENDIX. Volterra-Type Operators -- NOTES AND HISTORICAL COMMENTS -- REFERENCES -- SUBJECT INDEX -- Backmatter |
| title_auth | Optimization : a theory of necessary conditions / |
| title_exact_search | Optimization : a theory of necessary conditions / |
| title_full | Optimization : a theory of necessary conditions / Lucien W. Neustadt. |
| title_fullStr | Optimization : a theory of necessary conditions / Lucien W. Neustadt. |
| title_full_unstemmed | Optimization : a theory of necessary conditions / Lucien W. Neustadt. |
| title_short | Optimization : |
| title_sort | optimization a theory of necessary conditions |
| title_sub | a theory of necessary conditions / |
| topic | Mathematical optimization. http://id.loc.gov/authorities/subjects/sh85082127 Optimisation mathématique. MATHEMATICS General. bisacsh MATHEMATICS Topology. bisacsh Mathematical optimization fast |
| topic_facet | Mathematical optimization. Optimisation mathématique. MATHEMATICS General. MATHEMATICS Topology. Mathematical optimization |
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