Deterministic approximation algorithms in computational convexity:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
1998
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, IV, 128 S. |
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MARC
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| 245 | 1 | 0 | |a Deterministic approximation algorithms in computational convexity |c Andreas Brieden |
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Record in the Search Index
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| adam_text |
TABLE OF CONTENTS
1. INTRODUCTION
. 1
1.1 COMPUTATIONAL CONVEXITY . 1
1.2 RADII, CONDITION NUMBERS, POSDEF-0- 1-MAX AND SIMPLICES
. 2
1.2.1 RADII AND NORM-MAXIMIZATION. 3
1.2.2 CONDITION NUMBERS AND POSDEF-O-L-MAX. 7
1.2.3 LARGEST SIMPLICES IN BODIES. 12
1.3 DETERMINISM VERSUS RANDOMIZATION. 15
1.4 ACKNOWLEDGMENTS. 16
2.
PRELIMINARIES. 17
2.1 CONVEX SETS, BASIC PROBLEMS AND POLY TOPES. 17
2.2 COMPUTING MODEL AND ALGORITHMIC THEORY OF CONVEX BODIES . 18
2.3 GEOMETRIC PROPERTIES OF RADII. 23
2.4 VOLUME FORMULAS AND LARGEST SIMPLICES IN ELLIPSOIDS. 26
3. APPROXIMATION OF RADII AND NORM-MAXIMIZATION
. 31
3.1 SOLUTION WITH RESPECT TO POLYTOPAL NORMS. 32
3.1.1 INRADIUS AND WIDTH. 32
3.1.2 CIRCUMRADIUS, DIAMETER AND NORM-MAXIMIZATION. 36
3.2 APPROXIMATION OF
LP UNIT BALLS BY POLYTOPES. 41
3.2.1 APPROXIMATION IN M-DIMENSIONAL SUBSPACES. 41
3.2.2 POLYNOMIAL SIZE APPROXIMATION. 46
3.2.3 IMPROVING THE PERFORMANCE BY USING HADAMARD MATRICES? 48
3.3 APPROXIMATION ALGORITHMS. 55
3.4 UPPER BOUNDS. 58
4. APPROXIMATION OF CONDITION NUMBERS AND POSDEF-0-1-MAX
. 63
4.1 CONDITION NUMBERS OF CONVEX BODIES. 63
4.1.1 COMPLEXITY OF COMPUTING CONDITION NUMBERS OF POLYTOPES 63
4.1.2 LOWER BOUNDS FOR (ORACLE-) POLYNOMIAL-TIME ALGORITHMS . 64
4.1.3 UPPER BOUNDS FOR ORACLE-POLYNOMIAL-TIME ALGORITHMS . . 66
BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/954474325
TABLE OF CONTENTS
4.2
APPROXIMATION OF POSDEF-O-L-MAXIMIZATION .
4.2.1 TRANSFORMING POSDEF-0-1-MAX TO SIMPLEX-WIDTH . .
4.2.2
SOLVING POSDEF-0- 1-MAX BY APPROXIMATING BOO.
5.
APPROXIMATION OF LARGEST SIMPLICES IN BODIES.
5.1 A LOWER BOUND FOR LARGEST SIMPLICES APPROXIMATION.
5.1.1 THE GEOMETRIC IDEA.
5.1.2 A MODIFIED SHALLOW-CUT ELLIPSOID ALGORITHM.
5.2 AN UPPER BOUND FOR LARGEST SIMPLICES APPROXIMATION.
5.2.1 MOTIVATION.
5.2.2 LARGE J-SIMPLICES IN NORMALIZED 'H-POLYTOPES OF POLYNO
MIAL SIZE.
APPENDIX
.
A.
ENTROPY IN BANACH SPACES.
B. JACOBI'S METHOD IN FINITE PRECISION
.
C. APPROXIMATION OF M{E\ J, N) IN FINITE PRECISION
REFERENCES.
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| indexdate | 2024-10-09T16:03:47Z |
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| language | English |
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| physical | XVIII, IV, 128 S. |
| publishDate | 1998 |
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| spelling | Brieden, Andreas 1969- Verfasser (DE-588)114847444 aut Deterministic approximation algorithms in computational convexity Andreas Brieden 1998 XVIII, IV, 128 S. txt rdacontent n rdamedia nc rdacarrier München, Techn. Univ., Diss., 1998 Konvexität (DE-588)4114284-6 gnd rswk-swf Algorithmische Geometrie (DE-588)4130267-9 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Berechnungskomplexität (DE-588)4134751-1 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Algorithmische Geometrie (DE-588)4130267-9 s Konvexität (DE-588)4114284-6 s Berechnungskomplexität (DE-588)4134751-1 s Algorithmus (DE-588)4001183-5 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008190918&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Brieden, Andreas 1969- Deterministic approximation algorithms in computational convexity Konvexität (DE-588)4114284-6 gnd Algorithmische Geometrie (DE-588)4130267-9 gnd Algorithmus (DE-588)4001183-5 gnd Berechnungskomplexität (DE-588)4134751-1 gnd |
| subject_GND | (DE-588)4114284-6 (DE-588)4130267-9 (DE-588)4001183-5 (DE-588)4134751-1 (DE-588)4113937-9 |
| title | Deterministic approximation algorithms in computational convexity |
| title_auth | Deterministic approximation algorithms in computational convexity |
| title_exact_search | Deterministic approximation algorithms in computational convexity |
| title_full | Deterministic approximation algorithms in computational convexity Andreas Brieden |
| title_fullStr | Deterministic approximation algorithms in computational convexity Andreas Brieden |
| title_full_unstemmed | Deterministic approximation algorithms in computational convexity Andreas Brieden |
| title_short | Deterministic approximation algorithms in computational convexity |
| title_sort | deterministic approximation algorithms in computational convexity |
| topic | Konvexität (DE-588)4114284-6 gnd Algorithmische Geometrie (DE-588)4130267-9 gnd Algorithmus (DE-588)4001183-5 gnd Berechnungskomplexität (DE-588)4134751-1 gnd |
| topic_facet | Konvexität Algorithmische Geometrie Algorithmus Berechnungskomplexität Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008190918&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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