Holdings: On minimal pairs of compact convex sets and of convex functions

On minimal pairs of compact convex sets and of convex functions:

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Bibliographic Details
Main Author:	Kassa, Semu Mitiku 1968- (Author)
Format:	Thesis Book
Language:	English
Published:	2002
Subjects:	Kompakte konvexe Menge Optimierungsproblem Nichtglatte Optimierung Polytop Konvexe Funktion Quasidifferenzierbare Funktion Hochschulschrift
Online Access:	Inhaltsverzeichnis
Physical Description:	VIII, 94 S. graph. Darst.

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MARC


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adam_text	ON MINIMAL PAIRS OF COMPACT CONVEX SETS AND OF CONVEX FUNCTIONS ZUR ERLANGUNG DES AKADEMISCHEN GRADES EINES DOKTORS DER WIRTSCHAFTSWISSENSCHAFTEN (DR. RER. POL.) VON DER FAKULTAT FIIR ~ WIRTSCHAFTSWISSENSCHAFTEN DER UNIVERSITAT FRIDERICIANA ZU KARLSRUHE (TH) GENEHMIGTE DISSERTATION VON SEMU MITIKU KASSA TAG DER MIINDLICHEN PRIIFUNG: 07.11.2002 REFERENT: PROF. DR. DIETHARD PALLASCHKE KOREFERENT: PROF. DR. KLAUS NEUMANN KOREFERENT: PROF. DR. STEPHAN DEMPE KARLSRUHE, 2002 TABLE OF CONTENTS TABLE OF CONTENTS II PREFACE IV KURZFASSUNG VI LIST OF NOTATIONS VII 1 INTRODUCTION 1 2 DEFINITIONS AND PRELIMINARY CONCEPTS 5 2.1 AFFINE AND CONVEX SETS 5 2.2 CONVEX POLYTOPES 10 2.3 CONVEX FUNCTIONS 14 2.4 AN OVERVIEW OF GENERALIZED DIFFERENTIALS 18 3 MINIMAL PAIRS OF COMPACT CONVEX SETS 25 3.1 BASIC NOTIONS AND PROPERTIES 25 .3.2 BLASCHKE ADDITION 28 3.3 REDUCTION ALGORITHM IN TWO DIMENSIONAL SPACES 36 3.3.1 HANDSCHUG S ALGORITHM 37 3.3.2 MINIMALITY OF VERTICES OF PAIRS OF POLYTOPES JN 1R 2 42 3.4 MINIMALITY IN ARBITRARY DIMENSION 44 3.4.1 A REDUCTION TECHNIQUE FOR PAIRS OF COMPACT CONVEX SETS IN ANY DI- MENSION 45 3.4.2 RELATIONSHIP BETWEEN MINIMALITY OF PAIRS OF POLYTOPES AND THEIR NUMBER OF VERTICES 47 3.4.3 SOME MINIMALITY CONDITIONS FOR PAIRS OF POLYTOPES 48 4 D.C. FUNCTIONS AND THEIR MINIMAL REPRESENTATIONS 58 4.1 PROPERTIES OF D.C. FUNCTIONS 58 4.2 MINIMAL D.C. FUNCTIONS 63 4.3 DIFFERENCES OF SUBHARMONIC FUNCTIONS 67 4.4 APPLICATION OF D.S.H. FUNCTIONS TO MINIMAL D.C. REPRESENTATION 72 4.5 APPLICATION TO MINIMAL PAIRS OF SETS 75 5 MINIMAL REPRESENTATIONS OF POLYHEDRAL FUNCTIONS 78 5.1 DEFINITIONS AND BASIC PROPERTIES 78 5.2 D.C. REPRESENTATION OF POLYHEDRAL FUNCTIONS 83 BIBLIOGRAPHY 87 INDEX 92
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indexdate	2024-07-09T19:19:46Z
institution	BVB
language	English
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spelling	Kassa, Semu Mitiku 1968- Verfasser (DE-588)124263348 aut On minimal pairs of compact convex sets and of convex functions von Semu Mitiku Kassa 2002 VIII, 94 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Karlsruhe, Univ., Diss., 2002 Kompakte konvexe Menge (DE-588)4164844-4 gnd rswk-swf Optimierungsproblem (DE-588)4390818-4 gnd rswk-swf Nichtglatte Optimierung (DE-588)4120798-1 gnd rswk-swf Polytop (DE-588)4175324-0 gnd rswk-swf Konvexe Funktion (DE-588)4139679-0 gnd rswk-swf Quasidifferenzierbare Funktion (DE-588)4176636-2 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Quasidifferenzierbare Funktion (DE-588)4176636-2 s Optimierungsproblem (DE-588)4390818-4 s DE-604 Nichtglatte Optimierung (DE-588)4120798-1 s Kompakte konvexe Menge (DE-588)4164844-4 s Konvexe Funktion (DE-588)4139679-0 s Polytop (DE-588)4175324-0 s GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010589143&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Kassa, Semu Mitiku 1968- On minimal pairs of compact convex sets and of convex functions Kompakte konvexe Menge (DE-588)4164844-4 gnd Optimierungsproblem (DE-588)4390818-4 gnd Nichtglatte Optimierung (DE-588)4120798-1 gnd Polytop (DE-588)4175324-0 gnd Konvexe Funktion (DE-588)4139679-0 gnd Quasidifferenzierbare Funktion (DE-588)4176636-2 gnd
subject_GND	(DE-588)4164844-4 (DE-588)4390818-4 (DE-588)4120798-1 (DE-588)4175324-0 (DE-588)4139679-0 (DE-588)4176636-2 (DE-588)4113937-9
title	On minimal pairs of compact convex sets and of convex functions
title_auth	On minimal pairs of compact convex sets and of convex functions
title_exact_search	On minimal pairs of compact convex sets and of convex functions
title_full	On minimal pairs of compact convex sets and of convex functions von Semu Mitiku Kassa
title_fullStr	On minimal pairs of compact convex sets and of convex functions von Semu Mitiku Kassa
title_full_unstemmed	On minimal pairs of compact convex sets and of convex functions von Semu Mitiku Kassa
title_short	On minimal pairs of compact convex sets and of convex functions
title_sort	on minimal pairs of compact convex sets and of convex functions
topic	Kompakte konvexe Menge (DE-588)4164844-4 gnd Optimierungsproblem (DE-588)4390818-4 gnd Nichtglatte Optimierung (DE-588)4120798-1 gnd Polytop (DE-588)4175324-0 gnd Konvexe Funktion (DE-588)4139679-0 gnd Quasidifferenzierbare Funktion (DE-588)4176636-2 gnd
topic_facet	Kompakte konvexe Menge Optimierungsproblem Nichtglatte Optimierung Polytop Konvexe Funktion Quasidifferenzierbare Funktion Hochschulschrift
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010589143&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT kassasemumitiku onminimalpairsofcompactconvexsetsandofconvexfunctions

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