Large scale linear and integer optimization: a unified approach
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Kluwer
1999
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XVII, 740 S. graph. Darst. |
| ISBN: | 9781461372585 9781461349754 0792382021 |
Staff View
MARC
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| 245 | 1 | 0 | |a Large scale linear and integer optimization |b a unified approach |c Richard Kipp Martin |
| 264 | 1 | |a Boston [u.a.] |b Kluwer |c 1999 | |
| 300 | |a XVII, 740 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 4 | |a Optimisation mathématique | |
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| 650 | 4 | |a Linear programming | |
| 650 | 4 | |a Mathematical optimization | |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
Preface
xv
Part I MOTIVATION
1
1
LINEAR AND INTEGER LINEAR
OPTIMIZATION
3
1.1
Introduction
3
1.2
Linear and Integer Linear Optimization
5
1.3
A Guided Tour of Applications
7
1.4
Special Structure
21
1.5
Linear and Integer Linear Programming Codes
25
1.6
Other Directions
28
1.7
Exercises
29
Part II THEORY
33
2
LINEAR SYSTEMS AND PROJECTION
35
2.1
Introduction
35
2.2
Projection for Equality Systems: Gaussian Elimination
36
2.3
Projection for Inequality Systems: Fourier-Motzkin Elimi¬
nation
39
2.4
Applications of Projection
46
2.5
Theorems of the Alternative
49
2.6
Duality Theory
57
2.7
Complementary Slackness
61
2.8
Sensitivity Analysis
65
2.9
Conclusion
75
2.10
Exercises
75
viii
Large Scale Linear and Integer Optimization
3
LINEAR SYSTEMS AND INVERSE
PROJECTION
81
3.1
Introduction SI
3.2
Deleting Constraints by Adding Variables
81
3.3
Dual Relationships
91
3.4
Sensitivity Analysis
93
3.5
Conclusion
99
3.6
Homework Exercises
100
4
INTEGER LINEAR SYSTEMS:
PROJECTION AND INVERSE PROJECTION
103
4.1
Introduction
103
4.2
Background Material
105
4.3
Solving A System of Congruence Equations
114
4.4
Integer Linear Equalities
122
4.5
Integer Linear Inequalities: Projection
124
4.6
Integer Linear Inequalities: Inverse Projection
127
4.7
Conclusion
136
4.8
Exercises
137
Part III ALGORITHMS
141
5
THE SIMPLEX ALGORITHM
143
5.1
Introduction
143
5.2
Motivation
143
5.3
Pivoting
147
5.4
Revised Simplex
154
5.5
Product Form of the Inverse
162
5.6
Degeneracy and Cycling
168
5.7
Complexity of the Simplex Algorithm
177
5.8
Conclusion
178
5.9
Exercises
178
6
MORE ON SIMPLEX
183
6.1
Introduction
183
6.2
Sensitivity Analysis
184
6.3
The Dual Simplex Algorithm
191
Contents ix
6.4 Simple
Upper Bounds and Special Structure
198
6.5
Finding a Starting Basis
201
6.6
Pivot Column Selection
205
6.7
Other Computational Issues
209
6.8
Conclusion
215
6.9
Exercises
216
7
INTERIOR POINT ALGORITHMS:
POLYHEDRAL TRANSFORMATIONS
219
7.1
Introduction
219
7.2
Protective Transformations
225
7.3
Karmarkar s Algorithm
231
7.4
Polynomial Termination
234
7.5
Purification, Standard Form and Sliding Objective
239
7.6 Affine
Polyhedral Transformations
243
7.7
Geometry of the Least Squares Problem
254
7.8
Conclusion
258
7.9
Exercises
258
8
INTERIOR POINT ALGORITHMS:
BARRIER METHODS
261
8.1
Introduction
261
8.2
Primal Path Following
266
8.3
Dual Path Following
272
8.4
Primal-Dual Path Following
277
8.5
Polynomial Termination of Path Following Algorithms
283
8.6
Relation to Polyhedral Transformation Algorithms
292
8.7
Predictor-Corrector Algorithms
297
8.8
Other Issues
300
8.9
Conclusion
306
8.10
Exercises
310
9
INTEGER PROGRAMMING
313
9.1
Introduction
313
9.2
Modeling with Integer Variables
314
9.3
Branch-and-Bound
319
9.4
Node and Variable Selection
324
Large Scale Linear and Integer Optimization
9.5
More General Branching
328
9.6
Conclusion
34]
9.7
Exercises
341
Part IV SOLVING LARGE SCALE PROBLEMS:
DECOMPOSITION METHODS
347
10
PROJECTION: BENDERS
DECOMPOSITION
349
10.1
Introduction
349
10.2
The Benders Algorithm
350
10.3
A Location Application
354
10.4
Dual Variable Selection
360
10.5
Conclusion
364
10.6
Exercises
365
11
INVERSE PROJECTION: DANTZIG-WOLFE
.
DECOMPOSITION
369
11.1
Introduction
369
11.2
Dantzig-Wolfe Decomposition
370
11.3
A Location Application
375
11.4
Taking Advantage of Block Angular Structure
384
11.5
Computational Issues
386
11.6
Conclusion
390
11.7
Exercises
391
12
LAGRANGIAN METHODS
393
12.1
Introduction
393
12.2
The Lagrangian Dual
394
12.3
Extension to Integer Programming
398
12.4*
Properties of the Lagrangian Dual
402
12.5
Optimizing the Lagrangian Dual
408
12.6
Computational Issues
426
12.7
A Decomposition Algorithm for Integer Programming
429
12.8
Conclusion
434
12.9
Exercises
435
Contents
Part V SOLVING LARGE SCALE PROBLEMS:
USING SPECIAL STRUCTURE
437
13
SPARSE METHODS
439
13.1
Introduction
439
13.2
LU
Decomposition
439
13.3
Sparse
LU
Update
446
13.4
Numeric Cholesky Factorization
462
13.5
Symbolic Cholesky Factorization
466
13.6
Storing Sparse Matrices
471
13.7
Programming Issues
472
13.8
Computational Results: Barrier versus Simplex
478
13.9
Conclusion
479
13.10
Exercises
480
14
NETWORK FLOW LINEAR PROGRAMS
481
14.1
Introduction
481
14.2
Totally Unimodular Linear Programs
482
14.3
Network Simplex Algorithm
493
14.4
Important Network Flow Problems
505
14.5
Almost Network Problems
513
14.6
Integer Polyhedra
515
14.7
Conclusion
523
14.8
Exercises
524
15
LARGE INTEGER PROGRAMS:
PREPROCESSING AND CUTTING PLANES
527
15.1
Formulation Principles and Techniques
527
15.2
Preprocessing
533
15.3
Cutting Planes
542
15.4
Branch-and-Cut
555
15.5
Lifting
557
15.6
Lagrangian Cuts
560
15.7
Integer Programming Test Problems
561
15.8
Conclusion
562
15.9
Exercises
563
xii
Large Scale Linear and Integer Optimization
16
LARGE INTEGER PROGRAMS:
PROJECTION AND INVERSE PROJECTION
565
16.1
Introduction
565
16.2
Auxiliary Variable Methods
573
16.3
A Projection Theorem
601
16.4
Branch-and-Pricc
601
16.5
Projection of Extended Formulations: Benders Decompo¬
sition Revisited
613
16.6
Conclusion
630
16.7
Exercises
630
Part VI APPENDIX
633
A POLYHEDRAL THEORY
635
A.I Introduction
635
A.
2
Concepts and Definitions
635
A.3 Faces of Polyhedra
640
A.
4
Finite Basis Theorems
645
A.
5
Inner Products, Subspaces and Orthogonal Subspaces
651
A.
6
Exercises
653
В
COMPLEXITY THEORY
657
B.I Introduction
657
B.2 Solution Sizes
660
B.3 The Turing Machine
661
B.4 Complexity Classes
663
B.5 Satisfiability
667
B.6 .yVP-Completeness
669
B.7 Complexity of Gaussian Elimination
670
B.8 Exercises
674
С
BASIC GRAPH THEORY
677
D
SOFTWARE AND TEST PROBLEMS
681
e
Notation
Contents
хш
References
687
AUTHOR INDEX
723
TOPIC INDEX
731
|
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| indexdate | 2024-07-09T18:30:47Z |
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| owner | DE-703 DE-384 DE-634 DE-83 DE-11 DE-706 DE-188 DE-91 DE-BY-TUM DE-1050 |
| owner_facet | DE-703 DE-384 DE-634 DE-83 DE-11 DE-706 DE-188 DE-91 DE-BY-TUM DE-1050 |
| physical | XVII, 740 S. graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Kluwer |
| record_format | marc |
| spelling | Martin, Richard Kipp Verfasser (DE-588)173298222 aut Large scale linear and integer optimization a unified approach Richard Kipp Martin Boston [u.a.] Kluwer 1999 XVII, 740 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Discrete programmering gtt Lineaire programmering gtt Optimaliseren gtt Optimisation mathématique Optimisation mathématique ram Programmation linéaire Programmation linéaire ram algorithme point intérieur inriac algorithme simplexe inriac méthode décomposition inriac optimisation mathématique inriac programmation linéaire inriac Linear programming Mathematical optimization Ganzzahlige lineare Optimierung (DE-588)4155949-6 gnd rswk-swf Lineare Optimierung (DE-588)4035816-1 gnd rswk-swf Digitale Nachrichtentechnik (DE-588)4224275-7 gnd rswk-swf Digitaltechnik (DE-588)4012303-0 gnd rswk-swf Kommunikationstechnik (DE-588)4031888-6 gnd rswk-swf Lineare Optimierung (DE-588)4035816-1 s DE-188 Ganzzahlige lineare Optimierung (DE-588)4155949-6 s Kommunikationstechnik (DE-588)4031888-6 s Digitaltechnik (DE-588)4012303-0 s DE-604 Digitale Nachrichtentechnik (DE-588)4224275-7 s Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008573923&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Martin, Richard Kipp Large scale linear and integer optimization a unified approach Discrete programmering gtt Lineaire programmering gtt Optimaliseren gtt Optimisation mathématique Optimisation mathématique ram Programmation linéaire Programmation linéaire ram algorithme point intérieur inriac algorithme simplexe inriac méthode décomposition inriac optimisation mathématique inriac programmation linéaire inriac Linear programming Mathematical optimization Ganzzahlige lineare Optimierung (DE-588)4155949-6 gnd Lineare Optimierung (DE-588)4035816-1 gnd Digitale Nachrichtentechnik (DE-588)4224275-7 gnd Digitaltechnik (DE-588)4012303-0 gnd Kommunikationstechnik (DE-588)4031888-6 gnd |
| subject_GND | (DE-588)4155949-6 (DE-588)4035816-1 (DE-588)4224275-7 (DE-588)4012303-0 (DE-588)4031888-6 |
| title | Large scale linear and integer optimization a unified approach |
| title_auth | Large scale linear and integer optimization a unified approach |
| title_exact_search | Large scale linear and integer optimization a unified approach |
| title_full | Large scale linear and integer optimization a unified approach Richard Kipp Martin |
| title_fullStr | Large scale linear and integer optimization a unified approach Richard Kipp Martin |
| title_full_unstemmed | Large scale linear and integer optimization a unified approach Richard Kipp Martin |
| title_short | Large scale linear and integer optimization |
| title_sort | large scale linear and integer optimization a unified approach |
| title_sub | a unified approach |
| topic | Discrete programmering gtt Lineaire programmering gtt Optimaliseren gtt Optimisation mathématique Optimisation mathématique ram Programmation linéaire Programmation linéaire ram algorithme point intérieur inriac algorithme simplexe inriac méthode décomposition inriac optimisation mathématique inriac programmation linéaire inriac Linear programming Mathematical optimization Ganzzahlige lineare Optimierung (DE-588)4155949-6 gnd Lineare Optimierung (DE-588)4035816-1 gnd Digitale Nachrichtentechnik (DE-588)4224275-7 gnd Digitaltechnik (DE-588)4012303-0 gnd Kommunikationstechnik (DE-588)4031888-6 gnd |
| topic_facet | Discrete programmering Lineaire programmering Optimaliseren Optimisation mathématique Programmation linéaire algorithme point intérieur algorithme simplexe méthode décomposition optimisation mathématique programmation linéaire Linear programming Mathematical optimization Ganzzahlige lineare Optimierung Lineare Optimierung Digitale Nachrichtentechnik Digitaltechnik Kommunikationstechnik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008573923&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT martinrichardkipp largescalelinearandintegeroptimizationaunifiedapproach |