Integer programming:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham
Springer
[2014]
|
| Schriftenreihe: | Graduate texts in mathematics
271 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xii, 456 Seiten Illustrationen, Diagramme |
| ISBN: | 9783319110073 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
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| 003 | DE-604 | ||
| 005 | 20201111 | ||
| 007 | t | ||
| 008 | 141008s2014 a||| |||| 00||| eng d | ||
| 020 | |a 9783319110073 |c hbk. |9 978-3-319-11007-3 | ||
| 035 | |a (OCoLC)899633555 | ||
| 035 | |a (DE-599)OBVAC12046549 | ||
| 040 | |a DE-604 |b ger |e rda | ||
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| 100 | 1 | |a Conforti, Michele |e Verfasser |0 (DE-588)171836677 |4 aut | |
| 245 | 1 | 0 | |a Integer programming |c Michele Conforti, Gérard Cornuéjols, Giacomo Zambelli |
| 264 | 1 | |a Cham |b Springer |c [2014] | |
| 264 | 4 | |c © 2014 | |
| 300 | |a xii, 456 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate texts in mathematics |v 271 | |
| 650 | 0 | 7 | |a Ganzzahlige Optimierung |0 (DE-588)4155950-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematik |0 (DE-588)4037944-9 |2 gnd |9 rswk-swf |
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| 689 | 0 | 2 | |a Diskrete Gruppe |0 (DE-588)4135541-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Ganzzahlige Optimierung |0 (DE-588)4155950-2 |D s |
| 689 | 1 | |5 DE-604 | |
| 700 | 1 | |a Cornuéjols, Gérard |d 1950- |e Verfasser |0 (DE-588)121146855 |4 aut | |
| 700 | 1 | |a Zambelli, Giacomo |e Verfasser |0 (DE-588)1063042356 |4 aut | |
| 776 | 1 | 8 | |i Erscheint auch als |n Online-Ausgabe, eBook |z 978-3-319-11008-0 |
| 830 | 0 | |a Graduate texts in mathematics |v 271 |w (DE-604)BV000000067 |9 271 | |
| 856 | 4 | 2 | |m Digitalisierung UB Augsburg - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027549731&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027549731 | ||
Datensatz im Suchindex
| _version_ | 1804152577898577920 |
|---|---|
| adam_text | Contents
1
Getting Started
1
1.1
Integer Programming
....................... 1
1.2
Methods for Solving Integer Programs
............. 5
1.2.1
The Branch-and-Bound Method
............
б
1.2.2
The Cutting Plane Method
............... 11
1.2.3
The Branch-and-Cut Method
.............. 15
1.3
Complexity
............................ 16
1.3.1
Problems, Instances, Encoding Size
........... 17
1.3.2
Polynomial Algorithm
.................. 18
1.3.3
Complexity Class NP
.................. 19
1.4
Convex Hulls and Perfect Formulations
............ 20
1.4.1
Example: A Two-Dimensional Mixed Integer Set
... 22
1.4.2
Example: A Two-Dimensional Pure Integer Set
.... 24
1.5
Connections to Number Theory
................. 25
1.5.1
The Greatest Common Divisor
............. 26
1.5.2
Integral Solutions to Systems of Linear Equations
. . 29
1.6
Further Readings
......................... 36
1.7
Exercises
............................. 38
2
Integer Programming Models
45
2.1
The Knapsack Problem
..................... 45
2.2
Comparing Formulations
..................... 46
2.3
Cutting Stock: Formulations with Many Variables
...... 48
2.4
Packing, Covering, Partitioning
................. 51
2.4.1
Set Packing and Stable Sets
............... 51
2.4.2
Strengthening Set Packing Formulations
........ 52
2.4.3
Set Covering and Transversals
............. 53
2.4.4
Set Covering on Graphs: Many Constraints
...... 55
vu
viii
CONTEN^
2.4.5
Set Covering with Many Variables: Crew Scheduling
.
2.4.6
Covering
Steiner
Triples
.................
jj
2.5
Generalized Set Covering: The Satisfiability Problem
.....
|
2.6
The Sudoku Game
........................
Î
2.7
The Traveling Salesman Problem
................ (
2.8
The Generalized Assignment Problem
.............
(j
2.9
The Mixing Set
..........................
І
2.10
Modeling Fixed Charges
.....................
і
2.10.1
Facility Location
.....................
2.10.2
Network Design
......................
2.11
Modeling Disjunctions
......................
2.12
The Quadratic Assignment Problem
and Fortet s linearization
....................
2.13
Further Readings
.........................
2.14
Exercises
.............................
3
Linear Inequalities and Polyhedra
3.1
Fourier Elimination
........................
3.2
Farkas
Lemma
..........................
3.3
Linear Programming
.......................
3.4 Affine,
Convex, and Conic Combinations
............
3.4.1
Linear Combinations, Linear Spaces
..........
3.4.2 Affine
Combinations,
Affine
Spaces
...........
3.4.3
Convex Combinations, Convex Sets
...........
3.4.4
Conic Combinations, Convex Cones
..........
3.5
Polyhedra and the Theorem of Minkowski—Weyl
.......
3.5.1
Minkowski—Weyl Theorem for Polyhedral Cones
. . .
3.5.2
Minkowski-Weyl Theorem for Polyhedra
........
3.6
Lineali
ty
Space and Recession Cone
..............
3.7
Implicit Equalities,
Affine
Hull, and Dimension
........
3.8
Faces
................................10
3.9
Minimal Representation and Facets
...............
IO*
3.10
Minimal Faces
..........................
Ш
3.11
Edges and Extreme Rays
....................10
3.12
Decomposition Theorem for Polyhedra
.............11
3.13
Encoding Size of Vertices, Extreme Rays, and Facets
.....11
3.14
Carathéodory s
Theorem
.....................
Ili
3.15
Projections
............................11
3.16
Polarity
..............................11:
CONTENTS ix
3.17
Further Readings
......................... 120
3.18
Exercises
............................. 124
4
Perfect Formulations
129
4.1
Properties of Integral Polyhedra
................ 130
4.2
Total Unimodularity
....................... 131
4.3
Networks
............................. 134
4.3.1
Circulations
........................ 135
4.3.2
Shortest Paths
...................... 137
4.3.3
Maximum Flow and Minimum Cut
........... 139
4.4
Matchings in Graphs
....................... 145
4.4.1
Augmenting Paths
.................... 146
4.4.2
Cardinality Bipartite Matchings
............ 147
4.4.3
Minimum Weight Perfect Matchings
in Bipartite Graphs
................... 149
4.4.4
The Matching Polytope
................. 150
4.5
Spanning Trees
.......................... 153
4.6
Total Dual Integrality
...................... 155
4.7
Submodular
Polyhedra
...................... 157
4.8
The Fundamental Theorem
of Integer Programming
..................... 159
4.8.1
An Example: The Mixing Set
.............. 161
4.8.2
Mixed Integer Linear Programming is in NP
..... 163
4.8.3
Polynomial Encoding of the Facets of the Integer Hull
165
4.9
Union of Polyhedra
........................ 166
4.9.1
Example: Modeling Disjunctions
............ 169
4.9.2
Example: All the Even Subsets of a Set
........ 170
4.9.3
Mixed Integer Linear Representability
......... 171
4.10
The Size of a Smallest Perfect Formulation
.......... 174
4.10.1
Rectangle Covering Bound
............... 177
4.10.2
An Exponential Lower-Bound for the Cut Polytope
. . 179
4.10.3
An Exponential Lower-Bound for the
Matching Polytope
.................... 181
4.11
Further Readings
......................... 182
4.12
Exercises
............................. 187
5
Split and
Gomory
Inequalities
195
5.1
Split Inequalities
......................... 195
5.1.1
Inequality Description of the Split Closure
....... 199
5.1.2
Polyhedrality of the Split Closure
............ 202
5.1.3
Split Rank
........................ 203
x
CONTENU
5.1.4
Gomory
s
Mixed Integer Inequalities
..........
5.1.5
Mixed Integer Rounding Inequalities
..........
5.2
Chvátal
Inequalities
.......................
2(j
5.2.1
The
Chvátal
Closure of a Pure Integer Linear Set
... 21
5.2.2
Chvátal
Rank
....................... 21
5.2.3
Chvátal
Inequalities for Other Forms
of the Linear System
...................
Щ
5.2.4
Gomory s Fractional Cuts
................
2J
5.2.5
Gomory s Lexicographic Method for Pure
Integer Programs
..................... 2
5.3
Gomory s Mixed Integer Cuts
..................
*>?
5.4
Lift-and-Project
.......................... 2
5.4.1
Lift-and-Project Rank for Mixed
0,1
Linear Programs
..................... 2
5.4.2
A Finite Cutting Plane Algorithm for Mixed
0, 1
Linear Programming
................... 2
5.5
Further Readings
......................... 2!
5.6
Exercises
............................. 2
6
Intersection Cuts and Corner Poly
hedra 2i
6.1
Corner Polyhedron
........................ 2
6.2
Intersection Cuts
.........................
2¿
6.2.1
The Gauge Function
................... 2
6.2.2
Maximal Lattice-Free Convex Sets
........... 2
6.3
Infinite Relaxations
........................ 2?
6.3.1
Pure Integer Infinite Relaxation
.............
2Ї
6.3.2
Continuous Infinite Relaxation
.............
2
6.3.3
The Mixed Integer Infinite Relaxation
......... 2
6.3.4
Trivial and Unique Liftings
............... 2 .
6.4
Further Readings
......................... 27
6.5
Exercises
............................. 21
7
Valid Inequalities for Structured Integer Programs 2fi
7.1
Cover Inequalities for the
0,1
Knapsack Problem
....... 28
7.2
Lifting
...............................
28s
7.2.1
Lifting Minimal Cover Inequalities
...........
2fc
7.2.2
Lifting Functions, Superadditivity, and Sequence
Independent Lifting
...................
2c
7.2.3
Sequence Independent Lifting for Minimal
Cover Inequalities
................. . . .
2i
CONTENTS xi
7 3
Flow Cover Inequalities
.....................291
7.4
Faces of the Symmetric Traveling Salesman Polytope
.....299
7.4.1
Separation of
Subtour
Elimination Constraints
.... 302
7.4.2
Comb Inequalities
.................... 303
7.4.3
Local Cuts
........................ 305
7.5
Equivalence Between Optimization
and Separation
..........................307
7.6
Further Readings
.........................311
7.7
Exercises
.............................315
8
Reformulations and
Relaxations
321
8.1
Lagrangian Relaxation
......................321
8.1.1
Examples
.........................324
8.1.2
Subgradient
Algorithm
..................326
8.2
Dantzig-Wolfe Reformulation
..................330
8.2.1
Problems with Block Diagonal Structure
........332
8.2.2
Column Generation
...................334
8.2.3
Branch-and-Price
.....................337
8.3
Benders Decomposition
.....................338
8.4
Further Readings
.........................341
8.5
Exercises
.............................344
9
Enumeration
351
9.1
Integer Programming in Fixed Dimension
...........351
9.1.1
Basis Reduction
..................... 352
9.1.2
The Flatness Theorem and Rounding Polytopes
. . . 358
9.1.3
Lenstra s Algorithm
................... 362
9.2
Implementing Branch-and-Cut
................. 364
9.3
Dealing with Symmetries
.................... 373
9.4
Further Readings
......................... 380
9.5
Exercises
............................. 383
10
Semidefinite Bounds
389
10.1
Semidefinite Relaxations
.....................389
10.2
Two Applications in Combinatorial Optimization
.......391
10.2.1
The Max-Cut Problem
..................391
10.2.2
The Stable Set Problem
.................393
10.3
The
Lovász—
Schrijver
Relaxation
................394
10.3.1
Semidefinite Versus Linear Relaxations
.........396
Xli
10.3.2
Connection
with
Lift-
and-Project
............ 39*
10.3.3
Iterating the
Lovász—
Schrijver
Procedure
.......
39í
10.4
The Sherali—Adams and Lasserre Hierarchies
.........
40i
10.4.1
The Sherali-Adams Hierarchy
..............
40(
10.4.2
The Lasserre Hierarchy
................. 40
10.5
Further Readings
......................... 405
10.6
Exercises
............................. 41
Bibliography
4
li
Index
44
The authors discussing the outline of the book
|
| any_adam_object | 1 |
| author | Conforti, Michele Cornuéjols, Gérard 1950- Zambelli, Giacomo |
| author_GND | (DE-588)171836677 (DE-588)121146855 (DE-588)1063042356 |
| author_facet | Conforti, Michele Cornuéjols, Gérard 1950- Zambelli, Giacomo |
| author_role | aut aut aut |
| author_sort | Conforti, Michele |
| author_variant | m c mc g c gc g z gz |
| building | Verbundindex |
| bvnumber | BV042109256 |
| classification_rvk | QH 100 SK 890 |
| classification_tum | WIR 017f |
| ctrlnum | (OCoLC)899633555 (DE-599)OBVAC12046549 |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV042109256 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T01:12:56Z |
| institution | BVB |
| isbn | 9783319110073 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027549731 |
| oclc_num | 899633555 |
| open_access_boolean | |
| owner | DE-83 DE-29T DE-384 DE-188 DE-706 DE-91 DE-BY-TUM DE-11 DE-92 DE-634 DE-739 |
| owner_facet | DE-83 DE-29T DE-384 DE-188 DE-706 DE-91 DE-BY-TUM DE-11 DE-92 DE-634 DE-739 |
| physical | xii, 456 Seiten Illustrationen, Diagramme |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Conforti, Michele Verfasser (DE-588)171836677 aut Integer programming Michele Conforti, Gérard Cornuéjols, Giacomo Zambelli Cham Springer [2014] © 2014 xii, 456 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 271 Ganzzahlige Optimierung (DE-588)4155950-2 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Diskrete Gruppe (DE-588)4135541-6 gnd rswk-swf Mathematik (DE-588)4037944-9 s Algorithmus (DE-588)4001183-5 s Diskrete Gruppe (DE-588)4135541-6 s DE-604 Ganzzahlige Optimierung (DE-588)4155950-2 s Cornuéjols, Gérard 1950- Verfasser (DE-588)121146855 aut Zambelli, Giacomo Verfasser (DE-588)1063042356 aut Erscheint auch als Online-Ausgabe, eBook 978-3-319-11008-0 Graduate texts in mathematics 271 (DE-604)BV000000067 271 Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027549731&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Conforti, Michele Cornuéjols, Gérard 1950- Zambelli, Giacomo Integer programming Graduate texts in mathematics Ganzzahlige Optimierung (DE-588)4155950-2 gnd Mathematik (DE-588)4037944-9 gnd Algorithmus (DE-588)4001183-5 gnd Diskrete Gruppe (DE-588)4135541-6 gnd |
| subject_GND | (DE-588)4155950-2 (DE-588)4037944-9 (DE-588)4001183-5 (DE-588)4135541-6 |
| title | Integer programming |
| title_auth | Integer programming |
| title_exact_search | Integer programming |
| title_full | Integer programming Michele Conforti, Gérard Cornuéjols, Giacomo Zambelli |
| title_fullStr | Integer programming Michele Conforti, Gérard Cornuéjols, Giacomo Zambelli |
| title_full_unstemmed | Integer programming Michele Conforti, Gérard Cornuéjols, Giacomo Zambelli |
| title_short | Integer programming |
| title_sort | integer programming |
| topic | Ganzzahlige Optimierung (DE-588)4155950-2 gnd Mathematik (DE-588)4037944-9 gnd Algorithmus (DE-588)4001183-5 gnd Diskrete Gruppe (DE-588)4135541-6 gnd |
| topic_facet | Ganzzahlige Optimierung Mathematik Algorithmus Diskrete Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027549731&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000067 |
| work_keys_str_mv | AT confortimichele integerprogramming AT cornuejolsgerard integerprogramming AT zambelligiacomo integerprogramming |