Black box optimization with exact subsolvers: a radial basis function algorithm for problems with convex constraints
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Logos Verlag Berlin
2016
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | iv, 114 Seiten Illustrationen 21 cm |
| ISBN: | 9783832543297 3832543295 |
Internformat
MARC
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| 245 | 1 | 0 | |a Black box optimization with exact subsolvers |b a radial basis function algorithm for problems with convex constraints |c vorgelegt von Christine Edman |
| 264 | 1 | |a Berlin |b Logos Verlag Berlin |c 2016 | |
| 300 | |a iv, 114 Seiten |b Illustrationen |c 21 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 502 | |b Dissertation |c Universität Trier |d 2016 | ||
| 650 | 0 | 7 | |a Globale Optimierung |0 (DE-588)4140067-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Radiale Basisfunktion |0 (DE-588)4380647-8 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
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|---|---|
| adam_text |
C ONTENTS
1 IN TROD U CTION 1
1.1 EXPENSIVE OPTIMIZATION P RO B LE M
S. 1
1.2 GLOBAL OPTIMIZATION METHODS
. 2
1.2.1 STOCHASTIC AND DETERMINISTIC M
ETHODS. 2
1.2.2 RESPONSE
SURFACES.
3
1.2.2.1 TYPES OF RESPONSE SURFACES
.
4
1.2.2.2 PRINCIPLES OF SELECTING THE NEXT EVALUATION POINT . . . 5
2 O P TIM IZATION M ETH O D S FOR EX P EN SIV E PROBLEM S 7
2.1 SURFACE M
ETHODS.
7
2.2 SURFACE METHODS WITH RADIAL BASIS FUNCTIONS
.
8
2.3 GUTMANN*S RBF M E TH O D
.
9
2.3.1 THE INTERPOLATING M O D E
L. 9
2.3.1.1 RADIAL BASIS FUNCTIONS AND POSITIVE DEFINITENESS OF
F U N C TIO N S
.
12
2.3.1.2 A SYSTEM OF LINEAR EQUATIONS TO BE SOLVED
.
14
2.3.2 A MEASURE OF BUM
PINESS.16
2.3.3 AUXILIARY PROBLEMS FOR THE NEXT SAMPLE POINT
.22
3 A N OP TIM IZED CHOICE O F P O IN TS TO B E EVALU ATED 27
3.1 THE SUBPROBLEMS: CHEAP GLOBAL OPTIMIZATION P RO B LE M S
.28
3.2 DISTANCES, PROPERTIES OF / (R) AND LOWER BOUNDS FOR SN(X)
.
31
3.2.1 MINIMAL AND MAXIMAL D ISTAN C ES
.
32
3.2.2 USEFUL PROPERTIES OF 4 (R) AND LOWER BOUNDS FOR SN(X)
.
33
3.2.2.1 GAUSSIANS, INVERSE MULTIQUADRICS, MULTIQUADRICS AND
CUBIC SPLINE: LOWER BOUNDS FOR SN( X ) .33
3.2.2.2 THIN PLATE SPLINE: LOWER BOUNDS FOR SN( X )
.
35
3.3 USEFUL PROPERTIES OF THE MATRIX 4 AND THE (INVERSE OF THE) MATRIX A
. 37
3.3.1 THE BEHAVIOUR OF G
.
37
3.3.2 THEORETICAL ASPECTS CONCERNING A ^ 4
.
39
3.4 COMPUTATION OF LOWER BOUNDS FOR THE AUXILIARY PROBLEM AND THE
WEIGHTED
AUXILIARY PRO B LEM
.46
3.4.1 LOWER BOUNDS IF A *
CH.46
3.4.2 LOWER BOUNDS IF A ^
4 .50
3.4.2.1 P RELIM
INARIES.50
3.4.2.2 COMPUTING LOWER BOUNDS
.
52
3.5 THE BRANCH AND BOUND ALGORITHM
.57
3.5.1 THE R O U TIN E
.58
3.5.2 CONVERGENCE OF THE BRANCH AND BOUND A LG O RITH M
.
61
4 B OX PARTITION IN G 65
4.1 THE PROBLEM
.65
4.2 GENERAL BISECTION OF D-DIMENSIONAL RECTANGLES
.
66
4.2.1 THE REGULAR D-DIMENSIONAL RECTANGLE
.
67
4.2.2 A GEOMETRICAL ESTIM
ATION.69
4.2.3 GENERAL RECTANGLE
.
70
5 G ENERAL CON VEX CON STRAIN TS
75
5.1 SCALING DOWN RECTANGLES
.
76
5.2 THE MODIFIED BRANCH AND BOUND ALGORITHM
.78
6 N UM ERICAL TE S TS 81
6.1 THE IMPLEMENTATION
.
81
6.1.1
INITIALISATION.
81
6.1.2 STOPPING C R I T E R I A
.82
6.1.3 C Y C LE
S.
84
6.1.4 SOLVING THE CONVEX SUBPROBLEM S
.
86
6.1.5 SORTING OF
BOXES.86
6.2 HOW TO USE THE C O D E
.
86
6.2.1 PARAMETERS FOR THE I N P U T
.
86
6.2.2 READING THE O U TP U
T.88
6.3 TEST INSTANCES AND RUNTIM
E.88
6.3.1 R U N TIM
E.
89
6.3.2 BOX CONSTRAINED P RO B LE M S
.
94
6.3.3 RESULTS: BOX CONSTRAINED PROBLEMS
.
94
6.3.4 BOX CONSTRAINED PROBLEMS WITH ADDITIONAL CONVEX CONSTRAINTS . 94
6.3.5 RESULTS: PROBLEMS WITH ADDITIONAL CONVEX C O N STRA IN TS
.
99
7 C ONCLUSION S 101
A T EST PROBLEM S 103
B IBLIOGRAPHY 107 |
| any_adam_object | 1 |
| author | Edman, Christine |
| author_facet | Edman, Christine |
| author_role | aut |
| author_sort | Edman, Christine |
| author_variant | c e ce |
| building | Verbundindex |
| bvnumber | BV043882504 |
| ctrlnum | (OCoLC)967250222 (DE-599)DNB1113117249 |
| dewey-full | 519.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.6 |
| dewey-search | 519.6 |
| dewey-sort | 3519.6 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Thesis Book |
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| indexdate | 2024-08-03T03:11:35Z |
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| institution_GND | (DE-588)1065538812 |
| isbn | 9783832543297 3832543295 |
| language | English |
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| physical | iv, 114 Seiten Illustrationen 21 cm |
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| spelling | Edman, Christine Verfasser aut Black box optimization with exact subsolvers a radial basis function algorithm for problems with convex constraints vorgelegt von Christine Edman Berlin Logos Verlag Berlin 2016 iv, 114 Seiten Illustrationen 21 cm txt rdacontent n rdamedia nc rdacarrier Dissertation Universität Trier 2016 Globale Optimierung (DE-588)4140067-7 gnd rswk-swf Radiale Basisfunktion (DE-588)4380647-8 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Globale Optimierung (DE-588)4140067-7 s Radiale Basisfunktion (DE-588)4380647-8 s DE-604 Logos Verlag Berlin (DE-588)1065538812 pbl X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=d7e3c0e89a274998b40984632b84e108&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=029292089&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Edman, Christine Black box optimization with exact subsolvers a radial basis function algorithm for problems with convex constraints Globale Optimierung (DE-588)4140067-7 gnd Radiale Basisfunktion (DE-588)4380647-8 gnd |
| subject_GND | (DE-588)4140067-7 (DE-588)4380647-8 (DE-588)4113937-9 |
| title | Black box optimization with exact subsolvers a radial basis function algorithm for problems with convex constraints |
| title_auth | Black box optimization with exact subsolvers a radial basis function algorithm for problems with convex constraints |
| title_exact_search | Black box optimization with exact subsolvers a radial basis function algorithm for problems with convex constraints |
| title_full | Black box optimization with exact subsolvers a radial basis function algorithm for problems with convex constraints vorgelegt von Christine Edman |
| title_fullStr | Black box optimization with exact subsolvers a radial basis function algorithm for problems with convex constraints vorgelegt von Christine Edman |
| title_full_unstemmed | Black box optimization with exact subsolvers a radial basis function algorithm for problems with convex constraints vorgelegt von Christine Edman |
| title_short | Black box optimization with exact subsolvers |
| title_sort | black box optimization with exact subsolvers a radial basis function algorithm for problems with convex constraints |
| title_sub | a radial basis function algorithm for problems with convex constraints |
| topic | Globale Optimierung (DE-588)4140067-7 gnd Radiale Basisfunktion (DE-588)4380647-8 gnd |
| topic_facet | Globale Optimierung Radiale Basisfunktion Hochschulschrift |
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