Optimization theory: a concise introduction
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey
World Scientific Publishing
[2018]
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | x, 223 Seiten |
| ISBN: | 9789813237643 |
Staff View
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Record in the Search Index
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| adam_text | Contents
Preface vii
1. Mathematical Preparations 1
1 Basics in Rn........................................ 1
2 Some Results of Linear Algebra...................... 15
3 Functions: Limits and Continuity.................... 27
4 Differentiation..................................... 34
2. Optimization Problems and Existence of Optimal Solutions 43
1 Optimization Problems............................... 43
2 Some Examples of Optimization Problems.............. 49
3 Existence of Optimal Solutions...................... 52
4 A Constructive Method ................................... 60
3. Necessary and Sufficient Conditions of Optimal Solutions 67
1 Unconstrained Problems.............................. 67
2 Problems with Equality Constraints ...................... 73
3 Problems with Equality and Inequality Constraints .... 87
4 Problems without Regularity of the Constraints..... 100
4. Problems with Convexity and Quasi-Convexity Conditions 111
1 Convex Sets and Convex Functions................... Ill
2 Optimization Problems under Convexity Conditions ... 128
3 Lagrange Duality................................... 135
4 Quasi-Convexity and Related Optimization Problems ... 140
IX
X
Optimization Theory — A Concise Introduction
5. Linear Programming 147
1 Standard and Canonical Forms........................... 147
2 Geometric Considerations and the Fundamental
Theorem of Linear Programming.......................... 151
3 The Simplex Method..................................... 170
3.1 General consideration........................... 170
3.2 Phase II........................................ 175
3.3 Phase I......................................... 186
3.4 Endless cycling*................................ 188
4 Sensitivity Analysis . ................................ 194
5 Duality Theory......................................... 203
Bibliography 217
Index 219
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:07:28Z |
| institution | BVB |
| isbn | 9789813237643 |
| language | English |
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| spelling | Yong, Jiongmin 1958- (DE-588)121010481 aut Optimization theory a concise introduction Jiongmin Yong, University of Central Florida, USA New Jersey World Scientific Publishing [2018] © 2018 x, 223 Seiten txt rdacontent n rdamedia nc rdacarrier Optimierung (DE-588)4043664-0 gnd rswk-swf Optimierung (DE-588)4043664-0 s DE-604 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030451276&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Yong, Jiongmin 1958- Optimization theory a concise introduction Optimierung (DE-588)4043664-0 gnd |
| subject_GND | (DE-588)4043664-0 |
| title | Optimization theory a concise introduction |
| title_auth | Optimization theory a concise introduction |
| title_exact_search | Optimization theory a concise introduction |
| title_full | Optimization theory a concise introduction Jiongmin Yong, University of Central Florida, USA |
| title_fullStr | Optimization theory a concise introduction Jiongmin Yong, University of Central Florida, USA |
| title_full_unstemmed | Optimization theory a concise introduction Jiongmin Yong, University of Central Florida, USA |
| title_short | Optimization theory |
| title_sort | optimization theory a concise introduction |
| title_sub | a concise introduction |
| topic | Optimierung (DE-588)4043664-0 gnd |
| topic_facet | Optimierung |
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