Nonlinear programming: an introduction
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
De Gruyter
2014
|
| Series: | de Gruyter Textbook
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| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis Klappentext |
| Item Description: | Literaturangaben |
| Physical Description: | X, 350 S. graph. Darst. 240 mm x 170 mm |
| ISBN: | 9783110315271 3110315270 9783110315288 |
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MARC
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| 245 | 1 | 0 | |a Nonlinear programming |b an introduction |c Peter Zörnig |
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| 300 | |a X, 350 S. |b graph. Darst. |c 240 mm x 170 mm | ||
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Record in the Search Index
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CONTENTS
PREFACE V
NOTATIONS IX
1 INTRODUCTION 1
1.1 THE MODEL 1
1.2 SPECIAL CASES AND APPLICATIONS 3
1.2.1 SEPARABLE PROBLEM 4
1.2.2 PROBLEM OF QUADRATIC OPTIMIZATION 8
1.2.3 FURTHER EXAMPLES OF PRACTICAL APPLICATIONS 12
1.3 COMPLICATIONS CAUSED BY NONLINEARITY 19
1.4 REFERENCES FOR CHAPTER
1 23
PART I THEORETICAL FOUNDATIONS
2 OPTIMALITY CONDITIONS 27
2.1 FEASIBLE DIRECTIONS 27
2.2 FIRST AND SECOND-ORDER OPTIMALITY CONDITIONS 33
3 THE CONVEX
OPTIMIZATION PROBLEM 41
3.1 CONVEX SETS 41
3.2 CONVEX AND CONCAVE FUNCTIONS 48
3.3 DIFFERENTIATE CONVEX FUNCTIONS 51
3.4 SUBGRADIENT AND DIRECTIONAL DERIVATIVE 53
3.5 MINIMA OF CONVEX AND CONCAVE FUNCTIONS 62
4 KARUSH-KUHN-TUCKER CONDITIONS
AND DUALITY 69
4.1 KARUSH-KUHN-TUCKER CONDITIONS 69
4.2 LAGRANGE FUNCTION AND DUALITY 81
4.3 THE WOLFE DUAL
PROBLEM 94
4.4 SECOND-ORDER OPTIMALITY CRITERIA 98
4.5 REFERENCES FOR PART
I 107
PART II SOLUTION METHODS
5 ITERATIVE PROCEDURES AND EVALUATION CRITERIA 111
6 UNIDIMENSIONAL MINIMIZATION 115
6.1 DELIMITATION OF THE SEARCH REGION 116
6.2 NEWTON'S METHOD 120
6.3 INTERPOLATION METHODS 126
6.4 ON THE USE OF THE METHODS IN PRACTICE 130
HTTP://D-NB.INFO/1036807630
VIII *
CONTENTS
7 UNRESTRICTED MINIMIZATION 131
7.1 ANALYSIS OF QUADRATIC FUNCTIONS 131
7.2 THE GRADIENT METHOD 137
7.3 MULTIDIMENSIONAL NEWTON'S METHOD 142
7.4 CONJUGATE DIRECTIONS AND QUASI-NEWTON METHODS
7.5 CYCLIC COORDINATE SEARCH TECHNIQUES 152
7.6 INEXACT LINE SEARCH 155
7.7 TRUST REGION METHODS 161
8 LINEARLY CONSTRAINED PROBLEMS 168
8.1 FEASIBLE DIRECTION METHODS 168
8.1.1 ROSEN'S GRADIENT PROJECTION METHOD
8.1.2 ZOUTENDIJK'S METHOD 176
8.1.3 ADVANCED TECHNIQUES: AN OUTLINE *
8.2 LINEAR EQUALITY CONSTRAINTS 185
9 QUADRATIC PROBLEMS 193
9.1 AN ACTIVE-SET METHOD 193
9.2 KARUSH-KUHN-TUCKER CONDITIONS 197
9.3 LEMKE'S METHOD 199
10 THE GENERAL
PROBLEM 205
10.1 THE PENALTY METHOD 205
10.2 THE BARRIER METHOD 216
10.3 SEQUENTIAL QUADRATIC PROGRAMMING 221
11 NONDIFFERENTIABLE AND GLOBAL
OPTIMIZATION 226
11.1 NONDIFFERENTIABLE OPTIMIZATION 226
11.1.1 EXAMPLES FOR NONDIFFERENTIABLE PROBLEMS 226
11.1.2 BASIC IDEAS OF RESOLUTION 231
11.1.3 THE CONCEPT OF BUNDLE METHODS 237
11.2 GLOBAL OPTIMIZATION 240
11.2.1 SPECIFIC CASES OF GLOBAL OPTIMIZATION 241
11.2.2 EXACT METHODS 242
11.2.3 HEURISTIC METHODS 249
11.3 REFERENCES AND SOFTWARE FOR PART II 254
APPENDIX: SOLUTIONS OF EXERCISES 258
REFERENCES 343
168
-180
INDEX 347
The book is an introduction to nonlinear programming, written for students from
the fields of applied mathematics, engineering, economy, computation etc. The
work deals with the theoretical foundations and solution methods, beginning with
the classical procedures and reaching up to "modern" methods like trust region
methods or procedures for nonlinear and global optimization. A comprehensive
bibliography including diverse web sites with information about nonlinear pro¬
gramming (in particular software) is presented. Without sacrificing the necessary
mathematical rigor, excessive formalisms are avoided. Several examples, exercises
(with detailed solutions) and applications are provided, making the text adequate
for individual studies.
didactic approach
many examples and solved exercises
comprehensive references
-
including web sites |
| any_adam_object | 1 |
| author | Zörnig, Peter 1955- |
| author_GND | (DE-588)1047567814 |
| author_facet | Zörnig, Peter 1955- |
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| author_sort | Zörnig, Peter 1955- |
| author_variant | p z pz |
| building | Verbundindex |
| bvnumber | BV041584646 |
| classification_rvk | QH 421 SK 870 |
| ctrlnum | (OCoLC)864508636 (DE-599)DNB1036807630 |
| dewey-full | 519.76 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.76 |
| dewey-search | 519.76 |
| dewey-sort | 3519.76 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| language | English |
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| spelling | Zörnig, Peter 1955- Verfasser (DE-588)1047567814 aut Nonlinear programming an introduction Peter Zörnig Berlin [u.a.] De Gruyter 2014 X, 350 S. graph. Darst. 240 mm x 170 mm txt rdacontent n rdamedia nc rdacarrier de Gruyter Textbook Literaturangaben Nichtlineare Optimierung (DE-588)4128192-5 gnd rswk-swf Nichtlineare Optimierung (DE-588)4128192-5 s DE-604 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4378241&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027029842&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 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=027029842&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Zörnig, Peter 1955- Nonlinear programming an introduction Nichtlineare Optimierung (DE-588)4128192-5 gnd |
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| title | Nonlinear programming an introduction |
| title_auth | Nonlinear programming an introduction |
| title_exact_search | Nonlinear programming an introduction |
| title_full | Nonlinear programming an introduction Peter Zörnig |
| title_fullStr | Nonlinear programming an introduction Peter Zörnig |
| title_full_unstemmed | Nonlinear programming an introduction Peter Zörnig |
| title_short | Nonlinear programming |
| title_sort | nonlinear programming an introduction |
| title_sub | an introduction |
| topic | Nichtlineare Optimierung (DE-588)4128192-5 gnd |
| topic_facet | Nichtlineare Optimierung |
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