Lectures on convex sets:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey [u.a.]
World Scientific
2015
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 405 S. |
| ISBN: | 9789814656689 9789814656696 |
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MARC
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Record in the Search Index
| _version_ | 1804153060115611648 |
|---|---|
| adam_text | Contents*
Preface v
Notation vii
0. Prerequisites 1
1. The affine structure of 3Rn 11
1.1 Planes..................................................... 11
1.2 Affine spans............................................. 37
1.3 Affine transformations................................... 57
2. Convex sets 71
2.1 Algebraic properties of convex sets........................ 71
2.2 Relative interior of convex sets........................... 78
2.3 Closure and relative boundary of convex sets .............. 93
3. Convex hulls 117
3.1 Algebraic properties of convex hulls...................... 117
3.2 Topological properties of convex hulls.................... 128
4. Convex cones and conic hulls 145
4.1 Convex cones.............................................. 145
4.2 Conic hulls .............................................. 161
5. Recession and normal directions 183
5.1 Recession cones........................................... 183
5.2 Linearity spaces.......................................... 197
X
Lectures on Convex Sets
5.3 Normal and barrier cones................................. 206
6. Support and separation properties 227
6.1 Bounds, supports, and asymptotes..........................227
6.2 Containing and supporting halfspaces......................235
6.3 Separation by hyperplanes and slabs...................241
7. The extreme structure of convex sets 255
7.1 Extreme faces.............................................255
7.2 Extreme representations...................................267
8. The exposed structure of convex sets 287
8.1 Exposed faces.............................................287
8.2 Exposed representations...................................299
9. Polyhedra 319
9.1 Intersections of halfspaces...............................319
9.2 Properties of polyhedra ..................................328
Solutions to Exercises 345
Bibliography 387
Author Index 399
Subject Index 403
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| any_adam_object | 1 |
| author | Soltan, Valeriu |
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| id | DE-604.BV042403506 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:20:36Z |
| institution | BVB |
| isbn | 9789814656689 9789814656696 |
| language | English |
| lccn | 015002770 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027839146 |
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| physical | X, 405 S. |
| publishDate | 2015 |
| publishDateSearch | 2015 |
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| publisher | World Scientific |
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| spelling | Soltan, Valeriu Verfasser (DE-588)170955494 aut Lectures on convex sets Valeriu Soltan, George Mason University, USA New Jersey [u.a.] World Scientific 2015 X, 405 S. txt rdacontent n rdamedia nc rdacarrier Convex sets Convex geometry Konvexe Geometrie (DE-588)4407260-0 gnd rswk-swf Konvexe Geometrie (DE-588)4407260-0 s DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027839146&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Soltan, Valeriu Lectures on convex sets Convex sets Convex geometry Konvexe Geometrie (DE-588)4407260-0 gnd |
| subject_GND | (DE-588)4407260-0 |
| title | Lectures on convex sets |
| title_auth | Lectures on convex sets |
| title_exact_search | Lectures on convex sets |
| title_full | Lectures on convex sets Valeriu Soltan, George Mason University, USA |
| title_fullStr | Lectures on convex sets Valeriu Soltan, George Mason University, USA |
| title_full_unstemmed | Lectures on convex sets Valeriu Soltan, George Mason University, USA |
| title_short | Lectures on convex sets |
| title_sort | lectures on convex sets |
| topic | Convex sets Convex geometry Konvexe Geometrie (DE-588)4407260-0 gnd |
| topic_facet | Convex sets Convex geometry Konvexe Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027839146&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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