08896cam a2201009Ia 4500
ocn227117250
OCoLC
OCoLC
20200717131828.0
m o d
cr bn|||||||||
080506s2005 ne ob 001 0 eng d
UCW
eng
pn
UCW
N$T
YDXCP
MERUC
UBY
E7B
OCLCQ
IDEBK
OCLCQ
OPELS
TEF
OCLCQ
OCLCF
OCLCQ
DEBSZ
UPM
FIE
OCLCQ
U3W
D6H
WYU
YOU
SOI
OCLCO
LEAUB
OCLCO
OCLCQ
DCT
OCLCO
ERF
OCLCO
WURST
VLY
GBA476971
bnb
75190863
144220175
441764166
505057892
647545753
772910106
1162454475
0444515070
(hbk.)
9780444515070
(hbk.)
0080459218
(electronic bk.)
9780080459219
(electronic bk.)
1280638117
9781280638114
9786610638116
661063811X
9780444515070
DEBSZ
414263243
GBVCP
802563775
NZ1
14675976
DEBSZ
482357983
AU@
000056660077
(OCoLC)227117250
(OCoLC)75190863
(OCoLC)144220175
(OCoLC)441764166
(OCoLC)505057892
(OCoLC)647545753
(OCoLC)772910106
(OCoLC)1162454475
QA402.5
.D57 2005a
MAT
042000
bisacsh
519.6
22
MAIN
Discrete optimization /
edited by K. Aardal, G.L. Nemhauser and R. Weismantel.
1st ed.
Amsterdam ;
Boston :
Elsevier,
2005.
1 online resource (xi, 607 pages).
text
txt
rdacontent
computer
c
rdamedia
online resource
cr
rdacarrier
data file
rda
Handbooks in operations research and management science,
0927-0507 ;
v. 12
Print version record.
Includes bibliographical references and index.
On the history of combinatorial optimization (till 1960) -- Computational integer programming and cutting planes -- The structure of group relaxations -- Integer programming, lattices, and results in fixed dimension -- Primal integer programming -- Balanced matrices -- Submodular function minimization -- Semidefinite programming and integer programming -- Algorithms for stochastic mixed-integer programming models -- Constraint programming.
The chapters of this Handbook volume covers nine main topics that are representative of recent theoretical and algorithmic developments in the field. In addition to the nine papers that present the state of the art, there is an article on the early history of the field. The handbook will be a useful reference to experts in the field as well as students and others who want to learn about discrete optimization. All of the chapters in this handbook are written by authors who have made significant original contributions to their topics. Herewith a brief introduction to the chapters of the handbook. "On the history of combinatorial optimization (until 1960)" goes back to work of Monge in the 18th century on the assignment problem and presents six problem areas: assignment, transportation, maximum flow, shortest tree, shortest path and traveling salesman. The branch-and-cut algorithm of integer programming is the computational workhorse of discrete optimization. It provides the tools that have been implemented in commercial software such as CPLEX and Xpress MP that make it possible to solve practical problems in supply chain, manufacturing, telecommunications and many other areas. "Computational integer programming and cutting planes" presents the key ingredients of these algorithms. Although branch-and-cut based on linear programming relaxation is the most widely used integer programming algorithm, other approaches are needed to solve instances for which branch-and-cut performs poorly and to understand better the structure of integral polyhedra. The next three chapters discuss alternative approaches. "The structure of group relaxations" studies a family of polyhedra obtained by dropping certain nonnegativity restrictions on integer programming problems. Although integer programming is NP-hard in general, it is polynomially solvable in fixed dimension. "Integer programming, lattices, and results in fixed dimension" presents results in this area including algorithms that use reduced bases of integer lattices that are capable of solving certain classes of integer programs that defy solution by branch-and-cut. Relaxation or dual methods, such as cutting plane algorithms, progressively remove infeasibility while maintaining optimality to the relaxed problem. Such algorithms have the disadvantage of possibly obtaining feasibility only when the algorithm terminates. Primal methods for integer programs, which move from a feasible solution to a better feasible solution, were studied in the 1960's but did not appear to be competitive with dual methods. However, recent development in primal methods presented in "Primal integer programming" indicate that this approach is not just interesting theoretically but may have practical implications as well. The study of matrices that yield integral polyhedra has a long tradition in integer programming. A major breakthrough occurred in the 1990's with the development of polyhedral and structural results and recognition algorithms for balanced matrices. "Balanced matrices" is a tutorial on the subject. Submodular function minimization generalizes some linear combinatorial optimization problems such as minimum cut and is one of the fundamental problems of the field that is solvable in polynomial time. "Submodular function minimization" presents the theory and algorithms of this subject. In the search for tighter relaxations of combinatorial optimization problems, semidefinite programming provides a generalization of linear programming that can give better approximations and is still polynomially solvable. This subject is discussed in "Semidefinite programming and integer programming". Many real world problems have uncertain data that is known only probabilistically. Stochastic programming treats this topic, but until recently it was limited, for computational reasons, to stochastic linear programs. Stochastic integer programming is now a high profile research area and recent developments are presented in "Algorithms for stochastic mixed-integer programming models". Resource constrained scheduling is an example of a class of combinatorial optimization problems that is not naturally formulated with linear constraints so that linear programming based methods do not work well. "Constraint programming" presents an alternative enumerative approach that is complementary to branch-and-cut. Constraint programming, primarily designed for feasibility problems, does not use a relaxation to obtain bounds. Instead nodes of the search tree are pruned by constraint propagation, which tightens bounds on variables until their values are fixed or their domains are shown to be empty.
English.
Mathematical optimization.
1155
Integer programming.
15142
Optimisation mathématique.
10644
Programmation en nombres entiers.
118075
MATHEMATICS
Optimization.
bisacsh
20108
Integer programming.
fast
(OCoLC)fst00975500
15142
Mathematical optimization.
fast
(OCoLC)fst01012099
1155
Diskrete Optimierung
gnd
2385
programmeren
programming
operationeel onderzoek
operations research
algoritmen
algorithms
optimalisatie
optimization
integer programmeren
integer programming
modelleren
modeling
discrete simulatie
discrete simulation
Operations Research
Programming, Programming Languages
Operationeel onderzoek
Programmeren, programmeertalen
Electronic books.
396
Aardal, K.
(Karen)
edt
15878
Nemhauser, George L.
edt
19796
Weismantel, Robert.
edt
118076
Print version:
Discrete optimization.
1st ed.
Amsterdam ; Boston : Elsevier, 2005
(OCoLC)56875489
Handbooks in operations research and management science ;
v. 12.
0927-0507
100416
https://www.sciencedirect.com/science/handbooks/09270507/12
ebrary
EBRY
ebr10138290
EBSCOhost
EBSC
166624
ProQuest MyiLibrary Digital eBook Collection
IDEB
63811
YBP Library Services
YANK
2487445
92
ATIST
428488
428488
0
0
0
0
EBook
elib
elib
2020-07-17
2020-07-17
2020-07-17
EBOOK