Constrained global optimization: algorithms and applications
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin u.a.
Springer
1987
|
| Series: | Lecture notes in computer science
268 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 143 S. |
| ISBN: | 3540180958 0387180958 |
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MARC
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| 245 | 1 | 0 | |a Constrained global optimization |b algorithms and applications |c P. M. Pardalos ; J. B. Rosen |
| 264 | 1 | |a Berlin u.a. |b Springer |c 1987 | |
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Record in the Search Index
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| adam_text |
Table of Contents
Chapter 1 Convex sets and functions 1
1.1 Convex sets 1
1.2 Linear and affine spaces 2
1.3 Convex hull 3
1.4 Convex and concave functions 4
1.5 Convex envelopes 6
1.6 Exercises 10
1.7 References 11
Chapter 2 Optimality conditions in nonlinear programming 13
2.1 Quadratic problems solvable in polynomially bounded time 16
2.2 Some general remarks 19
2.3 Exercises : 20
2.4 References 21
Chapter 3 Combinatorial optimization problems that can be formu¬
lated as nonconvex quadratic problems 24
3.1 Integer programming 24
3.2 Quadratic 0 1 programming 25
3.3 Quadratic assignment problem 26
3.4 The 3 dimensional assignment problem 27
3.5 Bilinear programming 28
3.6 Linear complementarity problems 28
3.7 Max min problems 30
3.8 Exercises 30
3.9 References 32
Chapter 4 Enumerative methods in nonconvex programming 34
4.1 Global concave minimization by ranking the extreme points 34
4.2 Construction of linear underestimating functions 37
4.3 An algorithm for the indefinite quadratic problem 39
4.4 Concave cost netwoik flow problems , 43
4.5 Exercises „ 44
4.6 References 46
Chapter 5 Cutting plane methods 49
5.1 Tuy's "cone splitting" method 49
5.2 General class of algorithms « 52
5.3 Outer and inner approximation methods 54
5.4 Exercises „ 55
5.5 References 56
Chapter 6 Branch and bound methods 58
6.1 Rectangular partitions and convex envelopes 58
6.2 Simplex partitions 61
6.3 A successive underestimation method 64
6.4 Techniques using special ordered sets 67
6.5 Factorable nonconvex programming 69
6.6 Exercises 71
6.7 References 72
Chapter 7 Bilinear programming methods for nonconvex quadratic
problems 75
7.1 Introduction 75
7.2 Maximization of convex quadratic functions 77
7.3 Jointly constrained bilinear problems 79
7.4 Exercises 81
7.5 References 82
Chapter 8 Large scale problems 84
8.1 Concave quadratic problems 84
8.2 Separable formulation 85
8.3 Linear underestimator and error bounds 86
8.4 Piecewise linear approximation and zero one integer formulation 90
8.5 Computational algorithm and analysis 94
8.6 Exercises 98
8.7 References 99
Chapter 9 Global minimization of indefinite quadratic problems 101
9.1 Introduction 101
9.2 Partition of the objective function 104
9.3 Approximate methods and error bounds 105
i
9.4 Branch and bound bisection techniques 107
9.5 Piecewise linear approximation 110
9.6 Algorithm and computational results 111
9.7 Concluding remarks 113
9.8 Exercises 114
9.9 References 115
Chapter 10 Test problems for global nonconvex quadratic program¬
ming algorithms 118
10.1 Introduction 118
10.2 Global minimum concave quadratic test problems 118
10.3 Generation of test problems with nonconvex (concave or indefinite)
quadratic objective function 120
10.4 Exercises 121
10.5 References 122
General references for constrained global optimization 123 |
| any_adam_object | 1 |
| author | Pardalos, Panos M. 1954- Rosen, J. B. |
| author_GND | (DE-588)115385827 |
| author_facet | Pardalos, Panos M. 1954- Rosen, J. B. |
| author_role | aut aut |
| author_sort | Pardalos, Panos M. 1954- |
| author_variant | p m p pm pmp j b r jb jbr |
| building | Verbundindex |
| bvnumber | BV000698184 |
| classification_rvk | SS 4800 |
| classification_tum | MAT 916f |
| ctrlnum | (OCoLC)230857887 (DE-599)BVBBV000698184 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV000698184 |
| illustrated | Not Illustrated |
| indexdate | 2025-01-10T15:06:05Z |
| institution | BVB |
| isbn | 3540180958 0387180958 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000435685 |
| oclc_num | 230857887 |
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| physical | VII, 143 S. |
| psigel | TUB-www |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in computer science |
| series2 | Lecture notes in computer science |
| spelling | Pardalos, Panos M. 1954- Verfasser (DE-588)115385827 aut Constrained global optimization algorithms and applications P. M. Pardalos ; J. B. Rosen Berlin u.a. Springer 1987 VII, 143 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in computer science 268 Globale Optimierung (DE-588)4140067-7 gnd rswk-swf Beschränkung (DE-588)4247482-6 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Globale Optimierung (DE-588)4140067-7 s Beschränkung (DE-588)4247482-6 s DE-604 Algorithmus (DE-588)4001183-5 s Rosen, J. B. Verfasser aut Lecture notes in computer science 268 (DE-604)BV000000607 268 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000435685&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pardalos, Panos M. 1954- Rosen, J. B. Constrained global optimization algorithms and applications Lecture notes in computer science Globale Optimierung (DE-588)4140067-7 gnd Beschränkung (DE-588)4247482-6 gnd Algorithmus (DE-588)4001183-5 gnd |
| subject_GND | (DE-588)4140067-7 (DE-588)4247482-6 (DE-588)4001183-5 |
| title | Constrained global optimization algorithms and applications |
| title_auth | Constrained global optimization algorithms and applications |
| title_exact_search | Constrained global optimization algorithms and applications |
| title_full | Constrained global optimization algorithms and applications P. M. Pardalos ; J. B. Rosen |
| title_fullStr | Constrained global optimization algorithms and applications P. M. Pardalos ; J. B. Rosen |
| title_full_unstemmed | Constrained global optimization algorithms and applications P. M. Pardalos ; J. B. Rosen |
| title_short | Constrained global optimization |
| title_sort | constrained global optimization algorithms and applications |
| title_sub | algorithms and applications |
| topic | Globale Optimierung (DE-588)4140067-7 gnd Beschränkung (DE-588)4247482-6 gnd Algorithmus (DE-588)4001183-5 gnd |
| topic_facet | Globale Optimierung Beschränkung Algorithmus |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000435685&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000607 |
| work_keys_str_mv | AT pardalospanosm constrainedglobaloptimizationalgorithmsandapplications AT rosenjb constrainedglobaloptimizationalgorithmsandapplications |