Holdings: Generalized convexity and vector optimization

Generalized convexity and vector optimization:

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Bibliographic Details
Main Authors:	Mishra, Shashi Kant (Author), Wang, Shouyang 1958- (Author), Lai, Kin Keung 1950- (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 2009
Series:	Nonconvex optimization and its applications 90
Subjects:	Vektoroptimierung - Konvexität Convex functions Convexity spaces Mathematical optimization Konvexität Mehrkriterielle Optimierung
Online Access:	Inhaltsverzeichnis
Item Description:	Literaturverz. S. 281 - 293
Physical Description:	IX, 294 S. 24 cm
ISBN:	9783540856702 9783540856719

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Record in the Search Index

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adam_text	CONTENTS 1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 NONLINEAR SYMMETRIC DUAL PAIR OF PROGRAMMING PROBLEMS . . . . . . . . 3 1.2 MOTIVATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1 CONVEX AND GENERALIZED CONVEX FUNCTIONS . . . . . . . . . . . . . . . . . . . . . 8 2.2 INVEX AND GENERALIZED INVEX FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . 10 2.4 UNIVEX AND RELATED FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.5 V -INVEX AND RELATED FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.6 FURTHER GENERALIZED CONVEX FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . 22 3 GENERALIZED TYPE I AND RELATED FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . 25 3.1 GENERALIZED TYPE I UNIVEX FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.2 NONDIFFERENTIABLE D TYPE I AND RELATED FUNCTIONS . . . . . . . . . . . . . . . 27 . . . . . 28 3.4 NONDIFFERENTIABLE CONTINUOUS-TIME ANALOGUE OF GENERALIZED TYPE I FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.5 GENERALIZED CONVEX FUNCTIONS IN COMPLEX SPACES . . . . . . . . . . . . . . . 32 3.6 SEMILOCALLY CONNECTED TYPE I FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . 33 3.7 ( , * , * , * )- V -TYPE-I AND RELATED N -SET FUNCTIONS . . . . . . . . . . . . . . . 36 . . . . . . . . . . . . . 38 3.9 NONSMOOTH INVEX AND RELATED FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . 40 3.10 TYPE I AND RELATED FUNCTIONS IN BANACH SPACES . . . . . . . . . . . . . . . . . 41 4 OPTIMALITY CONDITIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.1 OPTIMALITY CONDITIONS FOR VECTOR OPTIMIZATION PROBLEMS . . . . . . . . . 45 4.2 OPTIMALITY CONDITIONS FOR NONDIFFERENTIABLE VECTOR OPTIMIZATION PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.3 OPTIMALITY CONDITIONS FOR MINIMAX FRACTIONAL PROGRAMS . . . . . . . . . 51 VII VIII CONTENTS 4.4 OPTIMALITY CONDITIONS FOR VECTOR OPTIMIZATION PROBLEMS ON BANACH SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.5 OPTIMALITY CONDITIONS FOR COMPLEX MINIMAX PROGRAMS ON COMPLEX SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.6 OPTIMALITY CONDITIONS FOR CONTINUOUS-TIME OPTIMIZATION PROBLEMS 60 4.7 OPTIMALITY CONDITIONS FOR NONDIFFERENTIABLE CONTINUOUS-TIME OPTIMIZATION PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.8 OPTIMALITY CONDITIONS FOR FRACTIONAL OPTIMIZATION PROBLEMS WITH SEMILOCALLY TYPE I PRE-INVEX FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . 73 4.9 OPTIMALITY CONDITIONS FOR VECTOR FRACTIONAL SUBSET OPTIMIZATION PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5 DUALITY THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 5.1 MONDWEIR TYPE DUALITY FOR VECTOR OPTIMIZATION PROBLEMS . . . . . . 91 5.2 GENERAL MONDWEIR TYPE DUALITY FOR VECTOR OPTIMIZATION PROBLEMS 94 5.3 MONDWEIR DUALITY FOR NONDIFFERENTIABLE VECTOR OPTIMIZATION PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 5.4 GENERAL MONDWEIR DUALITY FOR NONDIFFERENTIABLE VECTOR OPTIMIZATION PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.5 MONDWEIR DUALITY FOR NONDIFFERENTIABLE VECTOR OPTIMIZATION PROBLEMS WITH D UNIVEX FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 5.6 GENERAL MONDWEIR DUALITY FOR NONDIFFERENTIABLE VECTOR OPTIMIZATION PROBLEMS WITH D UNIVEX FUNCTIONS . . . . . . . . . . . . . . . 105 5.7 MONDWEIR DUALITY FOR NONDIFFERENTIABLE VECTOR OPTIMIZATION PROBLEMS WITH D TYPE-I UNIVEX FUNCTIONS . . . . . . . . . . . . . . . . . . . . . 107 5.8 GENERAL MONDWEIR DUALITY FOR NONDIFFERENTIABLE VECTOR OPTIMIZATION PROBLEMS WITH D TYPE-I UNIVEX FUNCTIONS . . . . . . . . . . 111 5.9 FIRST DUALITY MODEL FOR FRACTIONAL MINIMAX PROGRAMS . . . . . . . . . . . . 114 5.10 SECOND DUALITY MODEL FOR FRACTIONAL MINIMAX PROGRAMS . . . . . . . . . 117 5.11 THIRD DUALITY MODEL FOR FRACTIONAL MINIMAX PROGRAMS . . . . . . . . . . . 119 5.12 MONDWEIR DUALITY FOR NONDIFFERENTIABLE VECTOR OPTIMIZATION PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 5.13 DUALITY FOR VECTOR OPTIMIZATION PROBLEMS ON BANACH SPACES . . . . . . 126 5.14 FIRST DUAL MODEL FOR COMPLEX MINIMAX PROGRAMS . . . . . . . . . . . . . . . 128 5.15 SECOND DUAL MODEL FOR COMPLEX MINIMAX PROGRAMS . . . . . . . . . . . . 132 5.16 MONDWEIR DUALITY FOR CONTINUOUSTIME VECTOR OPTIMIZATION PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 5.17 GENERAL MONDWEIR DUALITY FOR CONTINUOUSTIME VECTOR OPTIMIZATION PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 5.18 DUALITY FOR NONDIFFERENTIABLE CONTINUOUSTIME OPTIMIZATION PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 5.19 DUALITY FOR VECTOR CONTROL PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 5.20 DUALITY FOR VECTOR FRACTIONAL SUBSET OPTIMIZATION PROBLEMS . . . . . . . 152 CONTENTS IX 6 SECOND AND HIGHER ORDER DUALITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 6.1 SECOND ORDER DUALITY FOR NONLINEAR OPTIMIZATION PROBLEMS . . . . . . . 165 6.2 SECOND ORDER DUALITY FOR MINIMAX PROGRAMS . . . . . . . . . . . . . . . . . . . 169 6.3 SECOND ORDER DUALITY FOR NONDIFFERENTIABLE MINIMAX PROGRAMS . . . 176 6.4 HIGHER ORDER DUALITY FOR NONLINEAR OPTIMIZATION PROBLEMS . . . . . . . 181 6.5 MONDWEIR HIGHER ORDER DUALITY FOR NONLINEAR OPTIMIZATION PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 6.6 GENERAL MONDWEIR HIGHER ORDER DUALITY FOR NONLINEAR OPTIMIZATION PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 6.7 MANGASARIAN TYPE HIGHER ORDER DUALITY FOR NONDIFFERENTIABLE OPTIMIZATION PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 6.8 MONDWEIR TYPE HIGHER ORDER DUALITY FOR NONDIFFERENTIABLE OPTIMIZATION PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 6.9 GENERAL MONDWEIR TYPE HIGHER ORDER DUALITY FOR NONDIFFERENTIABLE OPTIMIZATION PROBLEMS . . . . . . . . . . . . . . . . . . . 195 7 SYMMETRIC DUALITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 7.1 HIGHER ORDER SYMMETRIC DUALITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 7.2 MONDWEIR TYPE HIGHER ORDER SYMMETRIC DUALITY . . . . . . . . . . . . . . 203 7.3 SELF DUALITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 7.4 HIGHER ORDER VECTOR NONDIFFERENTIABLE SYMMETRIC DUALITY . . . . . . . . 210 7.5 MINIMAX MIXED INTEGER OPTIMIZATION PROBLEMS . . . . . . . . . . . . . . . . . 214 7.6 MIXED SYMMETRIC DUALITY IN NONDIFFERENTIABLE VECTOR OPTIMIZATION PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 7.7 MONDWEIR TYPE MIXED SYMMETRIC FIRST AND SECOND ORDER DUALITY IN NONDIFFERENTIABLE OPTIMIZATION PROBLEMS . . . . . . . . . . . . . 224 7.8 SECOND ORDER MIXED SYMMETRIC DUALITY IN NONDIFFERENTIABLE VECTOR OPTIMIZATION PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 7.9 SYMMETRIC DUALITY FOR A CLASS OF NONDIFFERENTIABLE VECTOR FRACTIONAL VARIATIONAL PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 8 VECTOR VARIATIONAL-LIKE INEQUALITY PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . 255 8.1 RELATIONSHIPS BETWEEN VECTOR VARIATIONAL-LIKE INEQUALITIES AND VECTOR OPTIMIZATION PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 8.2 ON RELATIONSHIPS BETWEEN VECTOR VARIATIONAL INEQUALITIES AND VECTOR OPTIMIZATION PROBLEMS WITH PSEUDO-UNIVEXITY . . . . . . . . . . . . 260 8.3 RELATIONSHIP BETWEEN VECTOR VARIATIONAL-LIKE INEQUALITIES AND NONDIFFERENTIABLE VECTOR OPTIMIZATION PROBLEMS . . . . . . . . . . . . . . . . 264 8.4 CHARACTERIZATION OF GENERALIZED UNIVEX FUNCTIONS . . . . . . . . . . . . . . . 269 8.5 CHARACTERIZATION OF NONDIFFERENTIABLE GENERALIZED INVEX FUNCTIONS . 275 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
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series	Nonconvex optimization and its applications
series2	Nonconvex optimization and its applications
spelling	Mishra, Shashi Kant Verfasser aut Generalized convexity and vector optimization Shashi Kant Mishra ; Shou-Yang Wang ; Kin Keung Lai Berlin [u.a.] Springer 2009 IX, 294 S. 24 cm txt rdacontent n rdamedia nc rdacarrier Nonconvex optimization and its applications 90 Literaturverz. S. 281 - 293 Vektoroptimierung - Konvexität Convex functions Convexity spaces Mathematical optimization Konvexität (DE-588)4114284-6 gnd rswk-swf Mehrkriterielle Optimierung (DE-588)4610682-0 gnd rswk-swf Mehrkriterielle Optimierung (DE-588)4610682-0 s Konvexität (DE-588)4114284-6 s DE-604 Wang, Shouyang 1958- Verfasser (DE-588)123314542 aut Lai, Kin Keung 1950- Verfasser (DE-588)131350609 aut Nonconvex optimization and its applications 90 (DE-604)BV010085908 90 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017373875&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Mishra, Shashi Kant Wang, Shouyang 1958- Lai, Kin Keung 1950- Generalized convexity and vector optimization Nonconvex optimization and its applications Vektoroptimierung - Konvexität Convex functions Convexity spaces Mathematical optimization Konvexität (DE-588)4114284-6 gnd Mehrkriterielle Optimierung (DE-588)4610682-0 gnd
subject_GND	(DE-588)4114284-6 (DE-588)4610682-0
title	Generalized convexity and vector optimization
title_auth	Generalized convexity and vector optimization
title_exact_search	Generalized convexity and vector optimization
title_full	Generalized convexity and vector optimization Shashi Kant Mishra ; Shou-Yang Wang ; Kin Keung Lai
title_fullStr	Generalized convexity and vector optimization Shashi Kant Mishra ; Shou-Yang Wang ; Kin Keung Lai
title_full_unstemmed	Generalized convexity and vector optimization Shashi Kant Mishra ; Shou-Yang Wang ; Kin Keung Lai
title_short	Generalized convexity and vector optimization
title_sort	generalized convexity and vector optimization
topic	Vektoroptimierung - Konvexität Convex functions Convexity spaces Mathematical optimization Konvexität (DE-588)4114284-6 gnd Mehrkriterielle Optimierung (DE-588)4610682-0 gnd
topic_facet	Vektoroptimierung - Konvexität Convex functions Convexity spaces Mathematical optimization Konvexität Mehrkriterielle Optimierung
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017373875&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV010085908
work_keys_str_mv	AT mishrashashikant generalizedconvexityandvectoroptimization AT wangshouyang generalizedconvexityandvectoroptimization AT laikinkeung generalizedconvexityandvectoroptimization

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