Linear optimization and extensions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1999
|
| Ausgabe: | 2., rev. and expanded ed. |
| Schriftenreihe: | Algorithms and combinatorics
12 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 457 - 494 |
| Beschreibung: | XX, 501 S. graph. Darst. |
| ISBN: | 3540658335 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV012608400 | ||
| 003 | DE-604 | ||
| 005 | 20000725 | ||
| 007 | t | ||
| 008 | 990608s1999 gw d||| |||| 00||| ger d | ||
| 020 | |a 3540658335 |c Pp. : DM 169.00 |9 3-540-65833-5 | ||
| 035 | |a (OCoLC)246595138 | ||
| 035 | |a (DE-599)BVBBV012608400 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a ger | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-29T |a DE-384 |a DE-824 |a DE-20 |a DE-91 |a DE-91G |a DE-898 |a DE-703 |a DE-634 |a DE-83 |a DE-11 |a DE-188 | ||
| 050 | 0 | |a T57.74 | |
| 082 | 0 | |a 519.72 | |
| 084 | |a QH 421 |0 (DE-625)141575: |2 rvk | ||
| 084 | |a SK 870 |0 (DE-625)143265: |2 rvk | ||
| 084 | |a MAT 912f |2 stub | ||
| 084 | |a 90C05 |2 msc | ||
| 084 | |a 65K05 |2 msc | ||
| 100 | 1 | |a Padberg, Manfred |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Linear optimization and extensions |c Manfred Padberg |
| 250 | |a 2., rev. and expanded ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1999 | |
| 300 | |a XX, 501 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Algorithms and combinatorics |v 12 | |
| 500 | |a Literaturverz. S. 457 - 494 | ||
| 650 | 4 | |a Lineare Optimierung - Algorithmentheorie | |
| 650 | 4 | |a Linear programming | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 0 | 7 | |a Lineare Optimierung |0 (DE-588)4035816-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Lineare Optimierung |0 (DE-588)4035816-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Algorithms and combinatorics |v 12 |w (DE-604)BV000617357 |9 12 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008563586&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-008563586 | ||
Datensatz im Suchindex
| _version_ | 1804127261028253696 |
|---|---|
| adam_text | Table of Contents
1. Introduction 1
1.1 Some Issues in Linear Computation 7
1.2 Three Examples of Linear Computation 13
1.2.1 Gargantuan Liquids, Inc 13
1.2.2 Oil Refineries, bpd 15
1.2.3 Save Berlin, usw 20
2. The Linear Programming Problem 25
2.1 Standard and Canonical Forms 26
2.2 Matrices, Vectors, Scalars 27
3. Basic Concepts 33
3.1 A Fundamental Theorem 36
3.2 Notational Conventions and Illustrations 39
4. Five Preliminaries 43
4.1 Bases and Basic Feasible Solutions 43
4.2 Detecting Optimality 43
4.3 Detecting Unboundedness 44
4.4 A Rank One Update 45
4.5 Changing Bases 45
5. Simplex Algorithms 49
5.1 Notation, Reading Instructions, Updating 50
5.2 Big M or How to Get Started 54
5.3 Selecting a Pivot Row and Column 56
5.4 Data Structures, Tolerances, Product Form 58
5.5 Equation Format and Cycling 63
5.6 Finiteness of a Simplex Algorithm 69
5.7 Canonical Form 71
5.7.1 A Worst Case Example for a Simplex Algorithm 75
5.8 Block Pivots and Structure 77
XVI Table of Contents
5.8.1 A Generalized Product Form 79
5.8.2 Upper Bounds 82
6. Primal Dual Pairs 87
6.1 Weak Duality 89
6.2 Strong Duality 91
6.2.1 Economic Interpretation and Applications 94
6.3 Solvability, Redundancy, Separability 97
6.4 A Dual Simplex Algorithm 103
6.4.1 Correctness, Finiteness, Initialization 105
6.5 Post Optimality 109
6.6 A Dynamic Simplex Algorithm 114
7. Analytical Geometry 121
7.1 Points, Lines, Subspaces 124
7.2 Polyhedra, Ideal Descriptions, Cones 131
7.2.1 Faces, Valid Equations, Affine Hulls 134
7.2.2 Facets, Minimal Complete Descriptions,
Quasi Uniqueness 138
7.2.3 Asymptotic Cones and Extreme Rays 141
7.2.4 Adjacency I, Extreme Rays of Polyhedra,
Homogenization 144
7.3 Point Sets, Affine Transformations, Minimal Generators 147
7.3.1 Displaced Cones, Adjacency II, Images of Polyhedra .. 150
7.3.2 Caratheodory, Minkowski, Weyl 155
7.3.3 Minimal Generators, Canonical Generators,
Quasi Uniqueness 157
7.4 Double Description Algorithms 165
7.4.1 Correctness and Finiteness of the Algorithm 168
7.4.2 Geometry, Euclidean Reduction, Analysis 173
7.4.3 The Basis Algorithm and All Integer Inversion 180
7.4.4 An All Integer Algorithm for Double Description 183
7.5 Digital Sizes of Rational Polyhedra and Linear Optimization . 188
7.5.1 Facet Complexity, Vertex Complexity, Complexity
of Inversion 190
7.5.2 Polyhedra and Related Polytopes for Linear
Optimization 194
7.5.3 Feasibility, Binary Search, Linear Optimization 197
7.5.4 Perturbation, Uniqueness, Separation 202
7.6 Geometry and Complexity of Simplex Algorithms 207
7.6.1 Pivot Column Choice, Simplex Paths, Big M Revisited 208
7.6.2 Gaussian Elimination, Fill in, Scaling 212
Table of Contents XVII
7.6.3 Iterative Step I, Pivot Choice, Cholesky Factorization . 216
7.6.4 Cross Multiplication, Iterative Step II, Integer
Factorization 219
7.6.5 Division Free Gaussian Elimination and Cramer s Rule 221
7.7 Circles, Spheres, Ellipsoids 229
8. Projective Algorithms 239
8.1 A Basic Algorithm 243
8.1.1 The Solution of the Approximate Problem 245
8.1.2 Convergence of the Approximate Iterates 246
8.1.3 Correctness, Finiteness, Initialization 250
8.2 Analysis, Algebra, Geometry 253
8.2.1 Solution to the Problem in the Original Space 254
8.2.2 The Solution in the Transformed Space 260
8.2.3 Geometric Interpretations and Properties 264
8.2.4 Extending the Exact Solution and Proofs 268
8.2.5 Examples of Projective Images 271
8.3 The Cross Ratio 274
8.4 Reflection on a Circle and Sandwiching 278
8.4.1 The Iterative Step 283
8.5 A Projective Algorithm 288
8.6 Centers, Barriers, Newton Steps 292
8.6.1 A Method of Centers 296
8.6.2 The Logarithmic Barrier Function 298
8.6.3 A Newtonian Algorithm 303
8.7 Coda 308
9. Ellipsoid Algorithms 309
9.1 Matrix Norms, Approximate Inverses, Matrix Inequalities ... 316
9.2 Ellipsoid Halving in Approximate Arithmetic 320
9.3 Polynomial Time Algorithms for Linear Programming 328
9.3.1 Linear Programming and Binary Search 336
9.4 Deep Cuts, Sliding Objective, Large Steps, Line Search 339
9.4.1 Linear Programming the Ellipsoidal Way:
Two Examples 344
9.4.2 Correctness and Finiteness of the DCS Ellipsoid
Algorithm 348
9.5 Optimal Separators, Most Violated Separators, Separation ... 352
9.6 e Solidification of Flats, Polytopal Norms, Rounding 356
9.6.1 Rational Rounding and Continued Fractions 361
9.7 Optimization and Separation 368
9.7.1 e Optimal Sets and e Optimal Solutions 371
XVIII Table of Contents
9.7.2 Finding Direction Vectors in the Asymptotic Cone.... 373
9.7.3 A CCS Ellipsoid Algorithm 375
9.7.4 Linear Optimization and Polyhedral Separation 378
10. Combinatorial Optimization: An Introduction 387
10.1 The Berlin Airlift Model Revisited 389
10.2 Complete Formulations and Their Implications 396
10.3 Extremal Characterizations of Ideal Formulations 405
10.3.1 Blocking and Antiblocking Polyhedra 414
10.4 Polyhedra with the Integrality Property 417
Appendices
A. Short Term Financial Management 423
B. Operations Management in a Refinery 427
C. Automatized Production: PCBs and Ulysses Problem .... 441
References 457
Bibliography 479
Index 495
|
| any_adam_object | 1 |
| author | Padberg, Manfred |
| author_facet | Padberg, Manfred |
| author_role | aut |
| author_sort | Padberg, Manfred |
| author_variant | m p mp |
| building | Verbundindex |
| bvnumber | BV012608400 |
| callnumber-first | T - Technology |
| callnumber-label | T57 |
| callnumber-raw | T57.74 |
| callnumber-search | T57.74 |
| callnumber-sort | T 257.74 |
| callnumber-subject | T - General Technology |
| classification_rvk | QH 421 SK 870 |
| classification_tum | MAT 912f |
| ctrlnum | (OCoLC)246595138 (DE-599)BVBBV012608400 |
| dewey-full | 519.72 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.72 |
| dewey-search | 519.72 |
| dewey-sort | 3519.72 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2., rev. and expanded ed. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01791nam a2200481 cb4500</leader><controlfield tag="001">BV012608400</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20000725 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">990608s1999 gw d||| |||| 00||| ger d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3540658335</subfield><subfield code="c">Pp. : DM 169.00</subfield><subfield code="9">3-540-65833-5</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)246595138</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV012608400</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">ger</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-29T</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-898</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">T57.74</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.72</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">QH 421</subfield><subfield code="0">(DE-625)141575:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 870</subfield><subfield code="0">(DE-625)143265:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 912f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">90C05</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">65K05</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Padberg, Manfred</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Linear optimization and extensions</subfield><subfield code="c">Manfred Padberg</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">2., rev. and expanded ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">1999</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XX, 501 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Algorithms and combinatorics</subfield><subfield code="v">12</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Literaturverz. S. 457 - 494</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Lineare Optimierung - Algorithmentheorie</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Linear programming</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical optimization</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Lineare Optimierung</subfield><subfield code="0">(DE-588)4035816-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Lineare Optimierung</subfield><subfield code="0">(DE-588)4035816-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Algorithms and combinatorics</subfield><subfield code="v">12</subfield><subfield code="w">(DE-604)BV000617357</subfield><subfield code="9">12</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008563586&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-008563586</subfield></datafield></record></collection> |
| id | DE-604.BV012608400 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:30:32Z |
| institution | BVB |
| isbn | 3540658335 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008563586 |
| oclc_num | 246595138 |
| open_access_boolean | |
| owner | DE-29T DE-384 DE-824 DE-20 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-898 DE-BY-UBR DE-703 DE-634 DE-83 DE-11 DE-188 |
| owner_facet | DE-29T DE-384 DE-824 DE-20 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-898 DE-BY-UBR DE-703 DE-634 DE-83 DE-11 DE-188 |
| physical | XX, 501 S. graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Springer |
| record_format | marc |
| series | Algorithms and combinatorics |
| series2 | Algorithms and combinatorics |
| spelling | Padberg, Manfred Verfasser aut Linear optimization and extensions Manfred Padberg 2., rev. and expanded ed. Berlin [u.a.] Springer 1999 XX, 501 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Algorithms and combinatorics 12 Literaturverz. S. 457 - 494 Lineare Optimierung - Algorithmentheorie Linear programming Mathematical optimization Lineare Optimierung (DE-588)4035816-1 gnd rswk-swf Lineare Optimierung (DE-588)4035816-1 s DE-604 Algorithms and combinatorics 12 (DE-604)BV000617357 12 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008563586&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Padberg, Manfred Linear optimization and extensions Algorithms and combinatorics Lineare Optimierung - Algorithmentheorie Linear programming Mathematical optimization Lineare Optimierung (DE-588)4035816-1 gnd |
| subject_GND | (DE-588)4035816-1 |
| title | Linear optimization and extensions |
| title_auth | Linear optimization and extensions |
| title_exact_search | Linear optimization and extensions |
| title_full | Linear optimization and extensions Manfred Padberg |
| title_fullStr | Linear optimization and extensions Manfred Padberg |
| title_full_unstemmed | Linear optimization and extensions Manfred Padberg |
| title_short | Linear optimization and extensions |
| title_sort | linear optimization and extensions |
| topic | Lineare Optimierung - Algorithmentheorie Linear programming Mathematical optimization Lineare Optimierung (DE-588)4035816-1 gnd |
| topic_facet | Lineare Optimierung - Algorithmentheorie Linear programming Mathematical optimization Lineare Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008563586&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000617357 |
| work_keys_str_mv | AT padbergmanfred linearoptimizationandextensions |