Verfügbarkeit: Linear optimization and extensions

Gespeichert in:

Bibliographische Detailangaben
Titel:	Linear optimization and extensions problems and solutions
Von:	Dimitris Alevras ; Manfred W. Padberg
Person:	Alevras, Dimitris Verfasser aut Padberg, Manfred W.
Hauptverfassende:	Alevras, Dimitris (VerfasserIn), Padberg, Manfred W. (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Berlin [u.a.] Springer 2001
Schriftenreihe:	Universitext
Schlagworte:	Lineare Optimierung - Lehrbuch Linear programming > Problems, exercises, etc Mathematical optimization > Problems, exercises, etc Lineare Optimierung
Online-Zugang:	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
Beschreibung:	IX, 449 S. graph. Darst.
ISBN:	3540417443

Internformat

MARC


LEADER	00000nam a22000008c 4500
001	BV013653048
003	DE-604
005	20080115
007	t\|
008	010320s2001 gw d\|\|\| \|\|\|\| 00\|\|\| eng d
016	7		\|a 961111526 \|2 DE-101
020			\|a 3540417443 \|9 3-540-41744-3
035			\|a (OCoLC)248715825
035			\|a (DE-599)BVBBV013653048
040			\|a DE-604 \|b ger \|e rakddb
041	0		\|a eng
044			\|a gw \|c DE
049			\|a DE-29T \|a DE-703 \|a DE-898 \|a DE-355 \|a DE-824 \|a DE-M347 \|a DE-706 \|a DE-384 \|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 90C05 \|2 msc
084			\|a 65K05 \|2 msc
084			\|a 17,1 \|2 ssgn
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
338			\|b nc \|2 rdacarrier
490	0		\|a Universitext
650		4	\|a Lineare Optimierung - Lehrbuch
650		4	\|a Linear programming \|v Problems, exercises, etc
650		4	\|a Mathematical optimization \|v Problems, exercises, etc
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
700	1		\|a Padberg, Manfred W. \|e Verfasser \|4 aut
856	4	2	\|m SWBplus Fremddatenuebernahme \|q application/pdf \|u 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 \|3 Inhaltsverzeichnis
943	1		\|a oai:aleph.bib-bvb.de:BVB01-009328643

Datensatz im Suchindex

DE-BY-OTHR_call_number	F 03/QH 421 A372
DE-BY-OTHR_katkey	3206632
DE-BY-OTHR_location	02
DE-BY-OTHR_media_number	067001073382 067001073439
DE-BY-UBR_call_number	80/SK 870 A372
DE-BY-UBR_katkey	3206632
DE-BY-UBR_location	UB Lesesaal Mathematik
DE-BY-UBR_media_number	069030186314
_version_	1835081313857568768
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 CRAMERS 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
any_adam_object	1
author	Alevras, Dimitris Padberg, Manfred W.
author_facet	Alevras, Dimitris Padberg, Manfred W.
author_role	aut aut
author_sort	Alevras, Dimitris
author_variant	d a da m w p mw mwp
building	Verbundindex
bvnumber	BV013653048
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
ctrlnum	(OCoLC)248715825 (DE-599)BVBBV013653048
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
format	Book
fullrecord	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01779nam a22004698c 4500</leader><controlfield tag="001">BV013653048</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20080115 </controlfield><controlfield tag="007">t\|</controlfield><controlfield tag="008">010320s2001 gw d\|\|\| \|\|\|\| 00\|\|\| eng d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">961111526</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3540417443</subfield><subfield code="9">3-540-41744-3</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)248715825</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV013653048</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">eng</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-703</subfield><subfield code="a">DE-898</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-M347</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-384</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">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="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Alevras, Dimitris</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="b">problems and solutions</subfield><subfield code="c">Dimitris Alevras ; Manfred W. Padberg</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">2001</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">IX, 449 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="0" ind2=" "><subfield code="a">Universitext</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Lineare Optimierung - Lehrbuch</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Linear programming</subfield><subfield code="v">Problems, exercises, etc</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical optimization</subfield><subfield code="v">Problems, exercises, etc</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="700" ind1="1" ind2=" "><subfield code="a">Padberg, Manfred W.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">SWBplus Fremddatenuebernahme</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=009328643&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-009328643</subfield></datafield></record></collection>
id	DE-604.BV013653048
illustrated	Illustrated
indexdate	2024-12-20T10:51:14Z
institution	BVB
isbn	3540417443
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-009328643
oclc_num	248715825
open_access_boolean
owner	DE-29T DE-703 DE-898 DE-BY-UBR DE-355 DE-BY-UBR DE-824 DE-M347 DE-706 DE-384 DE-634 DE-83 DE-11 DE-188
owner_facet	DE-29T DE-703 DE-898 DE-BY-UBR DE-355 DE-BY-UBR DE-824 DE-M347 DE-706 DE-384 DE-634 DE-83 DE-11 DE-188
physical	IX, 449 S. graph. Darst.
publishDate	2001
publishDateSearch	2001
publishDateSort	2001
publisher	Springer
record_format	marc
series2	Universitext
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

Verfügbarkeit

Per Ortsleihe bestellen

Inhaltsverzeichnis

Ausleihbestand Seybothstrasse

Bestandsangaben von Ausleihbestand Seybothstrasse
Signatur:	F 03 QH 421 A372 Lageplan
Exemplar 1	uneingeschränkt entleihbar Am Standort
Exemplar 2	uneingeschränkt entleihbar Am Standort

An UBR ausleihen
Ausleihen an der UBR sind mit eigenem Ausweis möglich.