Linear optimization and extensions: problems and solutions
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2001
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 449 S. graph. Darst. |
| ISBN: | 3540417443 |
Internformat
MARC
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| 100 | 1 | |a Alevras, Dimitris |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Linear optimization and extensions |b problems and solutions |c Dimitris Alevras ; Manfred W. Padberg |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2001 | |
| 300 | |a IX, 449 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 700 | 1 | |a Padberg, Manfred W. |e Verfasser |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804128463930523648 |
|---|---|
| adam_text | CONTENTS 1 INTRODUCTION 1 1.1 MINICASES AND EXERCISES . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 1 2 THE LINEAR
PROGRAMMING PROBLEM 39 2.1 EXERCISES . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 40 3 BASIC CONCEPTS 47
3.1 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 49 4 FIVE PRELIMINARIES 55 4.1 EXERCISES . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 57 5 SIMPLEX ALGORITHMS 63 5.1 EXERCISES . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 6
PRIMAL-DUAL PAIRS 93 6.1 EXERCISES . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . 100 7 ANALYTICAL
GEOMETRY 125 7.1 POINTS, LINES, SUBSPACES . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 125 7.2 POLYHEDRA, IDEAL
DESCRIPTIONS, CONES . . . . . . . . . . . . . . . . . . . . . . . . . .
. 127 7.2.1 FACES, VALID EQUATIONS, AFFINE HULLS . . . . . . . . . . . .
. . . . . . . . . . . . 128 7.2.2 FACETS, MINIMAL COMPLETE DESCRIPTIONS,
QUASI-UNIQUENESS . . . . . . . . . . 129 7.2.3 ASYMPTOTIC CONES AND
EXTREME RAYS . . . . . . . . . . . . . . . . . . . . . . . 130 7.2.4
ADJACENCY I, EXTREME RAYS OF POLYHEDRA, HOMOGENIZATION . . . . . . . . .
. . 130 7.3 POINT SETS, AFFINE TRANSFORMATIONS, MINIMAL GENERATORS . . .
. . . . . . . . . . . . . 131 7.3.1 DISPLACED CONES, ADJACENCY II,
IMAGES OF POLYHEDRA . . . . . . . . . . . . . . 132 7.3.2 CARATH ´
EODORY, MINKOWSKI, WEYL . . . . . . . . . . . . . . . . . . . . . . . .
. . 133 7.3.3 MINIMAL GENERATORS, CANONICAL GENERATORS, QUASI-UNIQUENESS
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
7.4 DOUBLE DESCRIPTION ALGORITHMS . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 135 7.4.1 CORRECTNESS AND FINITENESS OF THE
ALGORITHM . . . . . . . . . . . . . . . . . . . 136 7.4.2 GEOMETRY,
EUCLIDEAN REDUCTION, ANALYSIS . . . . . . . . . . . . . . . . . . . .
137 7.4.3 THE BASIS ALGORITHM AND ALL-INTEGER INVERSION . . . . . . . .
. . . . . . . . . . 138 7.4.4 AN ALL-INTEGER ALGORITHM FOR DOUBLE
DESCRIPTION . . . . . . . . . . . . . . . . . 139 7.5 DIGITAL SIZES OF
RATIONAL POLYHEDRA AND LINEAR OPTIMIZATION . . . . . . . . . . . . . .
140 7.5.1 FACET COMPLEXITY, VERTEX COMPLEXITY, COMPLEXITY OF INVERSION .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 141 7.5.2 POLYHEDRA AND RELATED POLYTOPES FOR LINEAR OPTIMIZATION . .
. . . . . . . . . 142 7.5.3 FEASIBILITY, BINARY SEARCH, LINEAR
OPTIMIZATION . . . . . . . . . . . . . . . . . 142 7.5.4 PERTURBATION,
UNIQUENESS, SEPARATION . . . . . . . . . . . . . . . . . . . . . . 144
7.6 GEOMETRY AND COMPLEXITY OF SIMPLEX ALGORITHMS . . . . . . . . . . .
. . . . . . . . . 146 7.6.1 PIVOT COLUMN CHOICE, SIMPLEX PATHS, BIG M
REVISITED . . . . . . . . . . . . . 147 7.6.2 GAUSSIAN ELIMINATION,
FILL-IN, SCALING . . . . . . . . . . . . . . . . . . . . . . 148 VIII
CONTENTS 7.6.3 ITERATIVE STEP I, PIVOT CHOICE, CHOLESKY FACTORIZATION .
. . . . . . . . . . . . . 149 7.6.4 CROSS MULTIPLICATION, ITERATIVE STEP
II, INTEGER FACTORIZATION . . . . . . . . . . 150 7.6.5 DIVISION FREE
GAUSSIAN ELIMINATION AND CRAMER*S RULE . . . . . . . . . . . . 151 7.7
CIRCLES, SPHERES, ELLIPSOIDS . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 153 7.8 EXERCISES . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . 156 8 PROJECTIVE
ALGORITHMS 201 8.1 A BASIC ALGORITHM . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . 203 8.1.1 THE SOLUTION OF THE
APPROXIMATE PROBLEM . . . . . . . . . . . . . . . . . . . . 203 8.1.2
CONVERGENCE OF THE APPROXIMATE ITERATES . . . . . . . . . . . . . . . .
. . . . . 205 8.1.3 CORRECTNESS, FINITENESS, INITIALIZATION . . . . . .
. . . . . . . . . . . . . . . . . 206 8.2 ANALYSIS, ALGEBRA, GEOMETRY .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 8.2.1
SOLUTION TO THE PROBLEM IN THE ORIGINAL SPACE . . . . . . . . . . . . .
. . . . . 207 8.2.2 THE SOLUTION IN THE TRANSFORMED SPACE . . . . . . .
. . . . . . . . . . . . . . . 209 8.2.3 GEOMETRIC INTERPRETATIONS AND
PROPERTIES . . . . . . . . . . . . . . . . . . . . . 211 8.2.4 EXTENDING
THE EXACT SOLUTION AND PROOFS . . . . . . . . . . . . . . . . . . . . .
214 8.2.5 EXAMPLES OF PROJECTIVE IMAGES . . . . . . . . . . . . . . . .
. . . . . . . . . . . 215 8.3 THE CROSS RATIO . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . 215 8.4 REFLECTION
ON A CIRCLE AND SANDWICHING . . . . . . . . . . . . . . . . . . . . . .
. . . 218 8.4.1 THE ITERATIVE STEP . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 220 8.5 A PROJECTIVE ALGORITHM . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 8.6
CENTERS, BARRIERS, NEWTON STEPS . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 223 8.6.1 A METHOD OF CENTERS . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 224 8.6.2 THE LOGARITHMIC
BARRIER FUNCTION . . . . . . . . . . . . . . . . . . . . . . . . . 226
8.6.3 A NEWTONIAN ALGORITHM . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 228 8.7 EXERCISES . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 230 9 ELLIPSOID
ALGORITHMS 263 9.1 MATRIX NORMS, APPROXIMATE INVERSES, MATRIX
INEQUALITIES . . . . . . . . . . . . . . . 265 9.2 ELLIPSOID *HALVING*
IN APPROXIMATE ARITHMETIC . . . . . . . . . . . . . . . . . . . . . .
266 9.3 POLYNOMIAL-TIME ALGORITHMS FOR LINEAR PROGRAMMING . . . . . . .
. . . . . . . . . . 269 9.4 DEEP CUTS, SLIDING OBJECTIVE, LARGE STEPS,
LINE SEARCH . . . . . . . . . . . . . . . . 272 9.4.1 LINEAR PROGRAMMING
THE ELLIPSOIDAL WAY: TWO EXAMPLES . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 274 9.4.2 CORRECTNESS AND FINITENESS
OF THE DCS ELLIPSOID ALGORITHM . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 277 9.5 OPTIMAL SEPARATORS, MOST
VIOLATED SEPARATORS, SEPARATION . . . . . . . . . . . . . . 278 9.6 *
-SOLIDIFICATION OF FLATS, POLYTOPAL NORMS, ROUNDING . . . . . . . . . .
. . . . . . . . 280 9.6.1 RATIONAL ROUNDING AND CONTINUED FRACTIONS . .
. . . . . . . . . . . . . . . . . 282 9.7 OPTIMIZATION AND SEPARATION .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 9.7.1
* -OPTIMAL SETS AND * -OPTIMAL SOLUTIONS . . . . . . . . . . . . . . . .
. . . . . 287 9.7.2 FINDING DIRECTION VECTORS IN THE ASYMPTOTIC CONE . .
. . . . . . . . . . . . . . 287 9.7.3 A CCS ELLIPSOID ALGORITHM . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 288 9.7.4 LINEAR
OPTIMIZATION AND POLYHEDRAL SEPARATION . . . . . . . . . . . . . . . . .
289 9.8 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 293 CONTENTS IX 10 COMBINATORIAL
OPTIMIZATION: AN INTRODUCTION 323 10.1THE BERLIN AIRLIFT MODEL REVISITED
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
10.2COMPLETE FORMULATIONS AND THEIR IMPLICATIONS . . . . . . . . . . . .
. . . . . . . . . 327 10.3EXTREMAL CHARACTERIZATIONS OF IDEAL
FORMULATIONS . . . . . . . . . . . . . . . . . . . 331 10.4POLYHEDRA
WITH THE INTEGRALITY PROPERTY . . . . . . . . . . . . . . . . . . . . .
. . . . . 334 10.5EXERCISES . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 336 APPENDICES A SHORT-TERM
FINANCIAL MANAGEMENT 359 A.1 SOLUTION TO THE CASH MANAGEMENT CASE . . .
. . . . . . . . . . . . . . . . . . . . . . 362 B OPERATIONS MANAGEMENT
IN A REFINERY 371 B.1 STEAM PRODUCTION IN A REFINERY . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . 371 B.2 THE OPTIMIZATION PROBLEM
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374
B.3 TECHNOLOGICAL CONSTRAINTS, PROFITS AND COSTS . . . . . . . . . . . .
. . . . . . . . . . 378 B.4 FORMULATION OF THE PROBLEM . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . 380 B.5 SOLUTION TO THE
REFINERY CASE . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 381 C AUTOMATIZED PRODUCTION: PCBS AND ULYSSES* PROBLEM 399 C.1
SOLUTIONS TO ULYSSES* PROBLEM . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 411 BIBLIOGRAPHY 431 INDEX 445
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:49:39Z |
| institution | BVB |
| isbn | 3540417443 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009328643 |
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| spelling | Alevras, Dimitris Verfasser aut Linear optimization and extensions problems and solutions Dimitris Alevras ; Manfred W. Padberg Berlin [u.a.] Springer 2001 IX, 449 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Lineare Optimierung - Lehrbuch Linear programming Problems, exercises, etc Mathematical optimization Problems, exercises, etc Lineare Optimierung (DE-588)4035816-1 gnd rswk-swf Lineare Optimierung (DE-588)4035816-1 s DE-604 Padberg, Manfred W. Verfasser aut SWBplus Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009328643&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Alevras, Dimitris Padberg, Manfred W. Linear optimization and extensions problems and solutions Lineare Optimierung - Lehrbuch Linear programming Problems, exercises, etc Mathematical optimization Problems, exercises, etc Lineare Optimierung (DE-588)4035816-1 gnd |
| subject_GND | (DE-588)4035816-1 |
| title | Linear optimization and extensions problems and solutions |
| title_auth | Linear optimization and extensions problems and solutions |
| title_exact_search | Linear optimization and extensions problems and solutions |
| title_full | Linear optimization and extensions problems and solutions Dimitris Alevras ; Manfred W. Padberg |
| title_fullStr | Linear optimization and extensions problems and solutions Dimitris Alevras ; Manfred W. Padberg |
| title_full_unstemmed | Linear optimization and extensions problems and solutions Dimitris Alevras ; Manfred W. Padberg |
| title_short | Linear optimization and extensions |
| title_sort | linear optimization and extensions problems and solutions |
| title_sub | problems and solutions |
| topic | Lineare Optimierung - Lehrbuch Linear programming Problems, exercises, etc Mathematical optimization Problems, exercises, etc Lineare Optimierung (DE-588)4035816-1 gnd |
| topic_facet | Lineare Optimierung - Lehrbuch Linear programming Problems, exercises, etc Mathematical optimization Problems, exercises, etc Lineare Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009328643&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT alevrasdimitris linearoptimizationandextensionsproblemsandsolutions AT padbergmanfredw linearoptimizationandextensionsproblemsandsolutions |