Optimization : : A Theory of Necessary Conditions / / Lucien W. Neustadt.
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...
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Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2015] ©1977 |
Year of Publication: | 2015 |
Language: | English |
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Physical Description: | 1 online resource (440 p.) |
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Neustadt, Lucien W., author. aut http://id.loc.gov/vocabulary/relators/aut Optimization : A Theory of Necessary Conditions / Lucien W. Neustadt. Princeton, NJ : Princeton University Press, [2015] ©1977 1 online resource (440 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Princeton Legacy Library ; 1374 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 restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021) Engineering Introductions and Overviews Engineering. Mathematical optimization. Technology & Engineering / General. bisacsh Title is part of eBook package: De Gruyter Princeton Legacy Lib. eBook Package 1931-1979 9783110426847 Title is part of eBook package: De Gruyter Princeton Legacy Lib. eBook Package Science 9783110413595 Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 9783110442496 print 9780691616834 https://doi.org/10.1515/9781400870530 https://www.degruyter.com/isbn/9781400870530 Cover https://www.degruyter.com/cover/covers/9781400870530.jpg |
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English |
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eBook |
author |
Neustadt, Lucien W., Neustadt, Lucien W., |
spellingShingle |
Neustadt, Lucien W., 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 |
author_facet |
Neustadt, Lucien W., Neustadt, Lucien W., |
author_variant |
l w n lw lwn l w n lw lwn |
author_role |
VerfasserIn VerfasserIn |
author_sort |
Neustadt, Lucien W., |
title |
Optimization : A Theory of Necessary Conditions / |
title_sub |
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_auth |
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_new |
Optimization : |
title_sort |
optimization : a theory of necessary conditions / |
series |
Princeton Legacy Library ; |
series2 |
Princeton Legacy Library ; |
publisher |
Princeton University Press, |
publishDate |
2015 |
physical |
1 online resource (440 p.) Issued also in print. |
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 |
isbn |
9781400870530 9783110426847 9783110413595 9783110442496 9780691616834 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA402 |
callnumber-sort |
QA 3402.5 N464 41976EB |
url |
https://doi.org/10.1515/9781400870530 https://www.degruyter.com/isbn/9781400870530 https://www.degruyter.com/cover/covers/9781400870530.jpg |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
514 - Topology |
dewey-full |
514/.64 |
dewey-sort |
3514 264 |
dewey-raw |
514/.64 |
dewey-search |
514/.64 |
doi_str_mv |
10.1515/9781400870530 |
oclc_num |
903318307 |
work_keys_str_mv |
AT neustadtlucienw optimizationatheoryofnecessaryconditions |
status_str |
n |
ids_txt_mv |
(DE-B1597)454413 (OCoLC)903318307 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter Princeton Legacy Lib. eBook Package 1931-1979 Title is part of eBook package: De Gruyter Princeton Legacy Lib. eBook Package Science Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 |
is_hierarchy_title |
Optimization : A Theory of Necessary Conditions / |
container_title |
Title is part of eBook package: De Gruyter Princeton Legacy Lib. eBook Package 1931-1979 |
_version_ |
1770176715714199552 |
fullrecord |
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