Holdings: Black box optimization with exact subsolvers

Black box optimization with exact subsolvers: a radial basis function algorithm for problems with convex constraints

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Bibliographic Details
Main Author:	Edman, Christine (Author)
Format:	Thesis Book
Language:	English
Published:	Berlin Logos Verlag Berlin 2016
Subjects:	Globale Optimierung Radiale Basisfunktion Hochschulschrift
Online Access:	Inhaltstext Inhaltsverzeichnis
Physical Description:	iv, 114 Seiten Illustrationen 21 cm
ISBN:	9783832543297 3832543295

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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 GUTMANNS 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
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author	Edman, Christine
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dewey-tens	510 - Mathematics
discipline	Mathematik
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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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