Algorithmic principles of mathematical programming:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
2002
|
| Series: | Kluwer texts in the mathematical sciences
24 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. 327-330) and index |
| Physical Description: | X, 337 S. Ill. |
| ISBN: | 140200852X 9781402008528 |
Staff View
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Record in the Search Index
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| adam_text | ALGORITHMIC PRINCIPLES OF MATHEMATICAL PROGRAMMING BY ULRICH FAIGLE
UNIVERSITY OF COLOGNE, COLOGNE, GERMANY WALTER KERN AND GEORG STILL
UNIVERSITY OFTWENTE, ENSCHEDE, THE NETHERLANDS KLUWER ACADEMIC
PUBLISHERS DORDRECHT / BOSTON / LONDON CONTENTS INTRODUCTION IX CHAPTER
1. REAL VECTOR SPACES 1 1.1. LINEAR AND AFFINE SPACES 1 1.2. MAPS AND
MATRICES 4 1.3. INNER PRODUCTS AND NORMS 7 1.4. CONTINUOUS AND
DIFFERENTIABLE FUNCTIONS 10 CHAPTER 2. LINEAR EQUATIONS AND LINEAR
INEQUALITIES 21 2.1. GAUSSIAN ELIMINATION 21 2.2. ORTHOGONAL PROJECTION
AND LEAST SQUARE APPROXIMATION 32 2.3. INTEGER SOLUTIONS OF LINEAR
EQUATIONS 40 2.4. LINEAR INEQUALITIES 45 CHAPTER 3. POLYHEDRA 55 3.1.
POLYHEDRAL CONES AND POLYTOPES 55 3.2. CONE DUALITY 59 3.3. POLAR
DUALITY OF CONVEX SETS 61 3.4. FACES 64 3.5. VERTICES AND POLYTOPES 67
3.6. RATIONAL POLYHEDRA 70 CHAPTER 4. LINEAR PROGRAMS AND THE SIMPLEX
METHOD 71 4.1. LINEAR PROGRAMS 71 4.2. THE SIMPLEX METHOD 80 4.3.
SENSITIVITY ANALYSIS 91 4.4. THE PRIMAL-DUAL SIMPLEX METHOD 93 CHAPTER
5. LAGRANGIAN DUALITY 95 5.1. LAGRANGIAN RELAXATION 95 5.2. LAGRANGIAN
DUALITY * 98 5.3. CONE DUALITY 103 5.4. OPTIMALITY CONDITIONS 105
CHAPTER 6. AN INTERIOR POINT ALGORITHM FOR LINEAR PROGRAMS 109 6.1. A
PRIMAL-DUAL RELAXATION 109 6.2. AN INTERIOR POINT METHOD 110 6.3.
CONSTRUCTING GOOD BASIC SOLUTIONS 115 VI CONTENTS 6.4. INITIALIZATION
AND RATIONAL LINEAR PROGRAMS 117 6.5. THE BARRIER POINT OF VIEW 120
CHAPTER 7. NETWORK FLOWS 123 7.1. GRAPHS 123 7.2. SHORTEST PATHS 130
7.3. MAXIMUM FLOW 139 7.4. MIN COST FLOWS 144 CHAPTER 8. COMPLEXITY 153
8.1. PROBLEMS AND INPUT SIZES 153 8.2. ALGORITHMS AND RUNNING TIMES 159
8.3. COMPLEXITY OF PROBLEMS 165 8.4. ARITHMETIC COMPLEXITY 172 CHAPTER
9. INTEGER PROGRAMMING 173 9.1. FORMULATING AN INTEGER PROGRAM 173 9.2.
CUTTING PLANES I 176 9.3. CUTTING PLANES II 182 9.4. BRANCH AND BOUND
185 9.5. LAGRANGIAN RELAXATION 187 9.6. DUALIZING THE BINARY CONSTRAINTS
194 CHAPTER 10. CONVEX SETS AND CONVEX FUNCTIONS 19 7 10.1. CONVEX SETS
197 . 10.2. CONVEX FUNCTIONS 203 10.3. CONVEX MINIMIZATION PROBLEMS 212
10.4. QUADRATIC PROGRAMMING 216 10.5. THE ELLIPSOID METHOD 223 10.6.
APPLICATIONS OF THE ELLIPSOID METHOD 230 CHAPTER 11. UNCONSTRAINED
OPTIMIZATION 241 11.1. OPTIMALITY CONDITIONS 242 11.2. DESCENT METHODS,
STEEPEST DESCENT 245 11.3. CONJUGATE DIRECTIONS 248 11.4. LINE SEARCH
253 11.5. NEWTON S METHOD 256 11.6. THE GAUSS-NEWTON METHOD 260 11.7.
QUASI-NEWTON METHODS 261 11.8. MINIMIZATION OF NONDIFFERENTIABLE
FUNCTIONS 266 CHAPTER 12. CONSTRAINED NONLINEAR OPTIMIZATION 273 12.1.
FIRST ORDER OPTIMALITY CONDITIONS 274 12.2. PRIMAL METHODS 285 12.3.
SECOND ORDER OPTIMALITY CONDITIONS AND SENSITIVITY 293 12.4. PENALTY AND
BARRIER METHODS 297 CONTENTS VII 12.5. KUHN-TUCKER METHODS 303 12.6.
SEMI-INFINITE AND SEMIDEFINITE PROGRAMS 310 LIST OF FREQUENTLY USED
SYMBOLS 325 BIBLIOGRAPHY 327 INDEX 331
|
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| dewey-full | 519.7 |
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| dewey-search | 519.7 |
| dewey-sort | 3519.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
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| indexdate | 2024-07-09T19:05:02Z |
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| isbn | 140200852X 9781402008528 |
| language | English |
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| physical | X, 337 S. Ill. |
| publishDate | 2002 |
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| publisher | Kluwer |
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| series | Kluwer texts in the mathematical sciences |
| series2 | Kluwer texts in the mathematical sciences |
| spelling | Faigle, Ulrich 1947- Verfasser (DE-588)135748410 aut Algorithmic principles of mathematical programming by Ulrich Faigle, Walter Kern and Georg Still Dordrecht [u.a.] Kluwer 2002 X, 337 S. Ill. txt rdacontent n rdamedia nc rdacarrier Kluwer texts in the mathematical sciences 24 Includes bibliographical references (p. 327-330) and index Algorithmes Programmation (Mathématiques) Algorithms Programming (Mathematics) Algorithmische Programmierung (DE-588)4293504-0 gnd rswk-swf Algorithmische Programmierung (DE-588)4293504-0 s DE-604 Kern, Walter 1957-2021 Verfasser (DE-588)13574850X aut Still, Georg 1951- Verfasser (DE-588)135748593 aut Kluwer texts in the mathematical sciences 24 (DE-604)BV005450041 24 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009959419&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Faigle, Ulrich 1947- Kern, Walter 1957-2021 Still, Georg 1951- Algorithmic principles of mathematical programming Kluwer texts in the mathematical sciences Algorithmes Programmation (Mathématiques) Algorithms Programming (Mathematics) Algorithmische Programmierung (DE-588)4293504-0 gnd |
| subject_GND | (DE-588)4293504-0 |
| title | Algorithmic principles of mathematical programming |
| title_auth | Algorithmic principles of mathematical programming |
| title_exact_search | Algorithmic principles of mathematical programming |
| title_full | Algorithmic principles of mathematical programming by Ulrich Faigle, Walter Kern and Georg Still |
| title_fullStr | Algorithmic principles of mathematical programming by Ulrich Faigle, Walter Kern and Georg Still |
| title_full_unstemmed | Algorithmic principles of mathematical programming by Ulrich Faigle, Walter Kern and Georg Still |
| title_short | Algorithmic principles of mathematical programming |
| title_sort | algorithmic principles of mathematical programming |
| topic | Algorithmes Programmation (Mathématiques) Algorithms Programming (Mathematics) Algorithmische Programmierung (DE-588)4293504-0 gnd |
| topic_facet | Algorithmes Programmation (Mathématiques) Algorithms Programming (Mathematics) Algorithmische Programmierung |
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