Finite dimensional convexity and optimization:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2001
|
| Series: | Studies in economic theory
13 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 147 - 150 |
| Physical Description: | XII, 154 S. graph. Darst. |
| ISBN: | 3540415165 |
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| 245 | 1 | 0 | |a Finite dimensional convexity and optimization |c Monique Florenzano ; Cuong Le Van |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2001 | |
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| 490 | 1 | |a Studies in economic theory |v 13 | |
| 500 | |a Literaturverz. S. 147 - 150 | ||
| 650 | 4 | |a Konvexe Optimierung | |
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Record in the Search Index
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| adam_text |
MONIQUE FLORENZANO * CUONG LE VAN IN COOPERATION WITH PASCAL GOURDEL
FINITE DIMENSIONAL CONVEXITY AND OPTIMIZATION WITH 9 FIGURES R CONTENTS
NOTATION XI 1. CONVEXITY IN R" 1 1.1 BASIC CONCEPTS 1 1.1.1 LINE
SEGMENT, CONVEX SET AND CONVEX HUELL 1 1.1.2 LINE, AFFINE SET AND AFFINE
HUELL 2 1.1.3 AFFINE MAPS 4 1.1.4 AFFINE INDEPENDENCE, BARYCENTRIC
COORDINATES, DIMENSION 5 1.1.5 HYPERPLANE 6 1.1.6 CONVEX CONE AND CONVEX
CONIC HUELL 7 1.2 TOPOLOGICAL PROPERTIES OF CONVEX SETS 8 1.2.1 CLOSURE
AND INTERIOR OF A CONVEX SET 8 1.2.2 RELATIVE INTERIOR AND RELATIVE
BOUNDARY OF A CONVEX SET 11 1.2.3 CONVEX HUELL OF A COMPACT SET 14
EXERCISES 15 2. SEPARATION AND POLARITY 21 2.1 SEPARATION OF CONVEX SETS
21 2.1.1 DEFINITIONS 21 2.1.2 PROJECTION ON A CLOSED CONVEX SET 22 2.1.3
SEPARATION THEOREMS 24 2.2 POLARS OF CONVEX SETS AND ORTHOGONAL
SUBSPACES 28 2.3 APPLICATION TO MINKOWSKI-FARKAS' LEMMA 29 2.3.1
MINKOWSKI-FARKAS' LEMMA 29 2.3.2 AND ITS COROLLARIES 32 EXERCISES 33 3.
EXTREMAL STRUCTURE OF CONVEX SETS 3 7 3.1 EXTREME POINTS AND FACES OF
CONVEX SETS 37 3.1.1 DEFINITIONS 37 3.1.2 KREIN-MILMAN'S THEOREM 38 3.2
APPLICATION TO LINEAR INEQUALITIES. WEYL'S THEOREM 40 3.3 EXTREME POINTS
AND EXTREMAL SUBSETS OF A POLYHEDRAL CONVEX SET 45 VIII CONTENTS
EXERCISES 47 4. LINEAR PROGRAMMING 51 4.1 NECESSARY AND SUFFICIENT
CONDITIONS OF OPTIMALITY 52 4.1.1 NECESSARY AND SUFFICIENT CONDITIONS OF
OPTIMALITY 52 4.1.2 APPLICATION TO SOLVING LINEAR PROGRAMMING PROBLEMS .
. 53 4.2 THE DUALITY THEOREM OF LINEAR PROGRAMMING 54 4.2.1 CANONICAL
FORM OF THE DUALITY THEOREM 54 4.2.2 GENERAL FORM OF THE DUALITY THEOREM
56 4.2.3 APPLICATION TO NONHOMOGENEOUS FARKAS' LEMMA 59 4.3 THE SIMPLEX
METHOD 60 4.3.1 EXTREME POINTS OF THE SET OF NONNEGATIVE SOLUTIONS TO A
SYSTEM OF LINEAR EQUATIONS 60 4.3.2 SOLVING A LINEAR PROGRAMMING PROBLEM
IN CANONICAL FORM 61 4.3.3 PIVOTING 62 4.3.4 PRACTICING THE SIMPLEX
METHOD 67 EXERCISES 67 5. CONVEX FUNCTIONS 73 5.1 BASIC DEFINITIONS AND
PROPERTIES 73 5.2 CONTINUITY THEOREMS 76 5.3 CONTINUITY PROPERTIES OF
COLLECTIONS OF CONVEX FUNCTIONS 79 EXERCISES 81 6. DIFFERENTIAL THEORY
OF CONVEX FUNCTIONS 87 6.1 THE HAHN-BANACH DOMINATED EXTENSION THEOREM
88 6.2 SUBLINEAR FUNCTIONS 89 6.3 SUPPORT FUNCTIONS 91 6.4 DIRECTIONAL
DERIVATIVES 92 6.5 SUBGRADIENTS AND SUBDIFFERENTIAL OF A CONVEX FUNCTION
93 6.6 DIFFERENTIABILITY OF CONVEX FUNCTIONS 98 6.7 DIFFERENTIAL
CONTINUITY FOR CONVEX FUNCTIONS 100 EXERCISES 104 7. CONVEX OPTIMIZATION
WITH CONVEX CONSTRAINTS 109 7.1 THE MINIMUM OF A CONVEX FUNCTION / : R*
* + R 110 7.2 KUHN-TUCKER CONDITIONS 111 7.2.1 NECESSARY AND SUFFICIENT
CONDITION FOR OPTIMALITY 111 7.2.2 LAGRANGIAN OF PROBLEM (P) 120 7.2.3
DUALITY IN CONVEX PROGRAMMING 122 7.3 VALUE FUNCTION 123 EXERCISES 125
CONTENTS IX 8. NON CONVEX OPTIMIZATION 129 8.1 QUASI-CONVEX FUNCTIONS
129 8.2 MINIMIZATION OF QUASI-CONVEX FUNCTIONS 134 8.3 DIFFERENTIABLE
OPTIMIZATION 137 EXERCISES 138 A. APPENDIX 141 A.L SOME PRELIMINARIES ON
TOPOLOGY 141 A.2 THE MEAN VALUE THEOREM 142 A.3 THE LOCAL INVERSION
THEOREM 142 A.4 THE IMPLICIT FUNCTIONS THEOREM 145 BIBLIOGRAPHY 147
INDEX 151 |
| any_adam_object | 1 |
| author | Florenzano, Monique 1937- Cuong Le Van 1946- |
| author_GND | (DE-588)170323927 (DE-588)122637410 |
| author_facet | Florenzano, Monique 1937- Cuong Le Van 1946- |
| author_role | aut aut |
| author_sort | Florenzano, Monique 1937- |
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| building | Verbundindex |
| bvnumber | BV013634204 |
| classification_rvk | QH 420 SK 870 |
| ctrlnum | (OCoLC)248422977 (DE-599)BVBBV013634204 |
| dewey-full | 515.8 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.8 |
| dewey-search | 515.8 |
| dewey-sort | 3515.8 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV013634204 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T06:40:28Z |
| institution | BVB |
| isbn | 3540415165 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009315010 |
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| physical | XII, 154 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer |
| record_format | marc |
| series | Studies in economic theory |
| series2 | Studies in economic theory |
| spelling | Florenzano, Monique 1937- Verfasser (DE-588)170323927 aut Finite dimensional convexity and optimization Monique Florenzano ; Cuong Le Van Berlin [u.a.] Springer 2001 XII, 154 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Studies in economic theory 13 Literaturverz. S. 147 - 150 Konvexe Optimierung Nichtlineare Optimierung / Mathematische Optimierung / Mathematische Ökonomie / Theorie Konvexe Optimierung (DE-588)4137027-2 gnd rswk-swf Konvexe Optimierung (DE-588)4137027-2 s DE-604 Cuong Le Van 1946- Verfasser (DE-588)122637410 aut Studies in economic theory 13 (DE-604)BV004683666 13 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009315010&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Florenzano, Monique 1937- Cuong Le Van 1946- Finite dimensional convexity and optimization Studies in economic theory Konvexe Optimierung Nichtlineare Optimierung / Mathematische Optimierung / Mathematische Ökonomie / Theorie Konvexe Optimierung (DE-588)4137027-2 gnd |
| subject_GND | (DE-588)4137027-2 |
| title | Finite dimensional convexity and optimization |
| title_auth | Finite dimensional convexity and optimization |
| title_exact_search | Finite dimensional convexity and optimization |
| title_full | Finite dimensional convexity and optimization Monique Florenzano ; Cuong Le Van |
| title_fullStr | Finite dimensional convexity and optimization Monique Florenzano ; Cuong Le Van |
| title_full_unstemmed | Finite dimensional convexity and optimization Monique Florenzano ; Cuong Le Van |
| title_short | Finite dimensional convexity and optimization |
| title_sort | finite dimensional convexity and optimization |
| topic | Konvexe Optimierung Nichtlineare Optimierung / Mathematische Optimierung / Mathematische Ökonomie / Theorie Konvexe Optimierung (DE-588)4137027-2 gnd |
| topic_facet | Konvexe Optimierung Nichtlineare Optimierung / Mathematische Optimierung / Mathematische Ökonomie / Theorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009315010&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004683666 |
| work_keys_str_mv | AT florenzanomonique finitedimensionalconvexityandoptimization AT cuonglevan finitedimensionalconvexityandoptimization |