Convex analysis and global optimization:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
1998
|
| Series: | Nonconvex optimization and its applications
22 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 339 S. graph. Darst. |
| ISBN: | 0792348184 |
Staff View
MARC
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Record in the Search Index
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| adam_text | CONVEX ANALYSIS AND GLOBAL OPTIMIZATION BY HOANG TUY INSTITUTE OF
MATHEMATICS, HANOI, VIETNAM KLUWER ACADEMIC PUBLISHERS DORDRECHT /
BOSTON / LONDON CONTENTS PREFACE IX PART I CONVEX ANALYSIS 1 1 CONVEX
SETS 3 1.1 AFFINE SETS 3 1.2 CONVEX SETS 6 1.3 RELATIVE INTERIOR AND
CLOSURE 8 1.4 CONVEX HUELL 13 1.5 SEPARATION THEOREMS 18 1.6 GEOMETRIE
STRUCTURE 21 1.7 REPRESENTATION OF CONVEX SETS , 26 1.8 POLARS OF CONVEX
SETS 28 1.9 POLYHEDRAL CONVEX SETS 30 1.10-EXERCISES 38 2 CONVEX
FUNCTIONS 41 2.1 DEFINITION AND BASIC PROPERTIES 41 2.2 CONVEXITY
PRESERVING OPERATIONS 46 2.3 LOWER SEMI-CONTINUITY 50 2.4 LIPSCHITZ
CONTINUITY 54 2.5 CONVEX INEQUALITIES 56 2.6 APPROXIMATION BY AFFINE
FUNCTIONS 60 2.7 SUBDIFFERENTIAL 62 2.8 SUBDIFFERENTIAL CALCULUS 67 2.9
APPROXIMATE SUBDIFFERENTIAL 69 *2.10 CONJUGATE FUNCTIONS 72 VI CONVEX
ANALYSIS AND GLOBAL OPTIMIZATION 2.11 EXTREMAL VALUES OF CONVEX
FUNCTIONS 74 2.12 SADDLE-FUNCTIONS AND MINIMAX 77 2.13 EXERCISES 80 3
D.C. FUNCTIONS AND D.C. SETS 83 3.1 D.C. FUNCTIONS 83 3.2 UNIVERSALITY
OF D.C.FUNCTIONS 85 3.3 D.C. REPRESENTATION OF BASIC COMPOSITE FUNCTIONS
88 3.4 D.C. REPRESENTATION OF SEPARABLE FUNCTIONS 93 3.5 D.C.
REPRESENTATION OF POLYNOMIALS 93 3.6 D.C. SETS 95 3.7 CONVEX MINORANTS
OF A D.C. FUNCTION 100 3.8 THE MINIMUM OF A D.C. FUNCTION 103 3.9
EXERCISES 105 PART II GLOBAL OPTIMIZATION 107 4 MOTIVATION AND OVERVIEW
109 4.1 GLOBAL VS LOCAL OPTIMUM 109 4.2 MULTIEXTREMALITY IN THE REAL
WORLD 110 4.3 BASIC CLASSES OF NONCONVEX PROBLEMS 115 4.4 GLOBAL
OPTIMALITY CRITERIA 117 4.5 DC INCLUSION ASSOCIATED WITH A FEASIBLE
SOLUTION 122 4.6 APPROXIMATE SOLUTION 123 4.7 WHEN IS GLOBAL
OPTIMIZATION MOTIVATED ? 125 4.8 EXERCISES 130 5 SUCCESSIVE PARTITIONING
METHODS 133 5.1 PARAMETRIC D.C. FEASIBILITY PROBLEMS 133 5.2 CONCAVITY
CUTS 136 5.3 SUBDIVISION PROCESSES 140 5.4 PROCEDURE DC 145 5.5 BRAUCH
AND SELECT ALGORITHMS 153 5.6 RECTANGULAR ALGORITHMS 159 5.7 REVERSE
CONVEX PROGRAMMING 164 5.8 EXERCISES 174 CONTENTS VII 6 OUTER AND INNER
APPROXIMATION 177 6.1 OUTER APPROXIMATION 177 6.2 CONCAVE MINIMIZATION
UNDER CONVEX CONSTRAINTS 181 6.3 CANONICAL DC PROGRAMMING 186 6.4
POLYHEDRAL ANNEXATION 192 6.5 DUALITY IN GLOBAL OPTIMIZATION 199 6.6
NONCANONICAL DC PROBLEMS 206 6.7 CONTINUOUS OPTIMIZATION 211 6.8
EXERCISES 220 7 DECOMPOSITION 223 7.1 MONOTONIE FUNCTIONS 223 7.2
DECOMPOSITION BY PROJECTION 227 7.3 DECOMPOSITION BY POLYHEDRAL
ANNEXATION 233 7.4 THE PARAMETRIC APPROACH 236 7.5 LINEAR MULTIPLICATIVE
PROGRAMMING 240 7.6 CONVEX CONSTRAINTS 247 7.7 REVERSE CONVEX
CONSTRAINTS 255 7.8 NETWORK CONSTRAINTS 261 7.9 SOME POLYNOMIAL-TIME
SOLVABLE PROBLEMS 269 7.10 EXERCISES 274 8 NONCONVEX QUADRATIC
PROGRAMMING 277 8.1 SOME BASIC PROPERTIES OF QUADRATIC FUNCTIONS 277 8.2
QUADRATIC MINIMIZATION OVER ELLIPSOIDS 281 8.3 GENERALIZED LINEAR
PROGRAMS 285 8.4 QUADRATIC PROBLEMS WITH CONVEX CONSTRAINTS 287 8.5
QUADRATIC PROBLEMS WITH QUADRATIC CONSTRAINTS 293 8.6 EXERCISES 316
REFERENCES 319 INDEX 337
|
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| dewey-search | 519.7/6 519.7/6 21 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| indexdate | 2024-07-09T18:24:00Z |
| institution | BVB |
| isbn | 0792348184 |
| language | English |
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| physical | XI, 339 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Kluwer |
| record_format | marc |
| series | Nonconvex optimization and its applications |
| series2 | Nonconvex optimization and its applications |
| spelling | Tuy, Hoang Verfasser aut Convex analysis and global optimization by Hoang Tuy Dordrecht [u.a.] Kluwer 1998 XI, 339 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Nonconvex optimization and its applications 22 Convex functions Convex sets Mathematical optimization Nonlinear programming Globale Optimierung (DE-588)4140067-7 gnd rswk-swf Konvexe Analysis (DE-588)4138566-4 gnd rswk-swf Globale Optimierung (DE-588)4140067-7 s DE-604 Konvexe Analysis (DE-588)4138566-4 s Nonconvex optimization and its applications 22 (DE-604)BV010085908 22 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008289325&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tuy, Hoang Convex analysis and global optimization Nonconvex optimization and its applications Convex functions Convex sets Mathematical optimization Nonlinear programming Globale Optimierung (DE-588)4140067-7 gnd Konvexe Analysis (DE-588)4138566-4 gnd |
| subject_GND | (DE-588)4140067-7 (DE-588)4138566-4 |
| title | Convex analysis and global optimization |
| title_auth | Convex analysis and global optimization |
| title_exact_search | Convex analysis and global optimization |
| title_full | Convex analysis and global optimization by Hoang Tuy |
| title_fullStr | Convex analysis and global optimization by Hoang Tuy |
| title_full_unstemmed | Convex analysis and global optimization by Hoang Tuy |
| title_short | Convex analysis and global optimization |
| title_sort | convex analysis and global optimization |
| topic | Convex functions Convex sets Mathematical optimization Nonlinear programming Globale Optimierung (DE-588)4140067-7 gnd Konvexe Analysis (DE-588)4138566-4 gnd |
| topic_facet | Convex functions Convex sets Mathematical optimization Nonlinear programming Globale Optimierung Konvexe Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008289325&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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