Maxima and minima with applications: practical optimization and duality
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Wiley
1999
|
| Series: | Wiley-Interscience series in discrete mathematics and optimization
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 284 S. graph. Darst. |
| ISBN: | 0471252891 |
Staff View
MARC
| LEADER | 00000nam a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV023775764 | ||
| 003 | DE-604 | ||
| 005 | 20101029 | ||
| 007 | t | ||
| 008 | 990520s1999 d||| |||| 00||| eng d | ||
| 020 | |a 0471252891 |9 0-471-25289-1 | ||
| 035 | |a (OCoLC)38992870 | ||
| 035 | |a (DE-599)BVBBV023775764 | ||
| 040 | |a DE-604 |b ger | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-634 | ||
| 050 | 0 | |a QA306 | |
| 082 | 0 | |a 511/.66 |2 21 | |
| 084 | |a SK 870 |0 (DE-625)143265: |2 rvk | ||
| 100 | 1 | |a Kaplan, Wilfred |d 1915- |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Maxima and minima with applications |b practical optimization and duality |c Wilfred Kaplan |
| 264 | 1 | |a New York [u.a.] |b Wiley |c 1999 | |
| 300 | |a X, 284 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Wiley-Interscience series in discrete mathematics and optimization | |
| 650 | 7 | |a Análise variacional |2 larpcal | |
| 650 | 7 | |a Maxima |2 gtt | |
| 650 | 7 | |a Minima (natuurwetenschappen) |2 gtt | |
| 650 | 7 | |a Optimaliseren |2 gtt | |
| 650 | 7 | |a Programação convexa |2 larpcal | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 4 | |a Maxima and minima | |
| 650 | 0 | 7 | |a Minimum |0 (DE-588)4467521-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Analytische Geometrie |0 (DE-588)4001867-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Maximum |0 (DE-588)4467522-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Optimierung |0 (DE-588)4043664-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Maximum |0 (DE-588)4467522-7 |D s |
| 689 | 0 | 1 | |a Minimum |0 (DE-588)4467521-5 |D s |
| 689 | 0 | 2 | |a Analytische Geometrie |0 (DE-588)4001867-2 |D s |
| 689 | 0 | 3 | |a Optimierung |0 (DE-588)4043664-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m GBV Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017417982&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-017417982 | ||
Record in the Search Index
| _version_ | 1804138965275508736 |
|---|---|
| adam_text | MAXIMA AND MINIMA WITH APPLICATIONS PRACTICAL OPTIMIZATION AND DUALITY
WILFRED KAPLAN EMERITUS PROFESSOR OF MATHEMATICS UNIVERSITY OF MICHIGAN
A WILEY-INTERSCIENCE PUBLICATION JOHN WILEY & SONS, INC. NEW YORK *
CHICHESTER * WEINHEIM * BRISBANE * SINGAPORE * TORONTO CONTENTS PREFACE
IX 1 MAXIMA AND MINIMA IN ANALYTIC GEOMETRY 1 1.1 MAXIMA AND MINIMA;
CASE OF FUNCTIONS OF ONE VARIABLE 1 PROBLEMS 1.1-1.5 5 1.2 CONVEXITY 6
1.3 CONVEXITY AND MAXIMA AND MINIMA 9 PROBLEMS 1.6-1.16 12 1.4 PROBLEMS
IN TWO DIMENSIONS 15 PROBLEMS 1.17-1.27 23 1.5 SOME GEOMETRIE EXTREMUM
PROBLEMS 26 PROBLEMS 1.28-1.36 30 1.6 GEOMETRY OF N-DIMENSIONAL SPACE 31
1.7 CONVEX FUNCTIONS OF N VARIABLES 36 1.8 QUADRATIC FORMS 38 PROBLEMS
1.37-1.55 41 1.9 CONVEXITY AND EXTREMA, LEVEL SETS AND SUBLEVEL SETS 45
PROBLEMS 1.56-1.63 49 1.10 STABILITY 50 1.11 GLOBAL ASYMPTOTIC
STABILITY, APPLICATION TO FINDING MINIMIZER 56 PROBLEMS 1.64-1.73 58
1.12 EXTREMA OF FUNCTIONS ON UNBOUNDED CLOSED SETS 60 1.13 SHORTEST
DISTANCE FROM A LINEAR VARIETY 63 PROBLEMS 1.74-1.84 66 1.14 OTHER INNER
PRODUCTS AND NORMS IN TV 68 1.15 MORE ON MINIMUM PROBLEMS FOR QUADRATIC
FUNCTIONS 71 PROBLEMS 1.85-1.93 74 1.16 PHYSICAL APPLICATIONS 76
PROBLEMS 1.94-1.96 78 1.17 BEST APPROXIMATION BY POLYNOMIALS 79 PROBLEMS
1.97-1.105 82 REFERENCES 83 CONTENTS 2 SIDE CONDITIONS 85 2.1 REVIEW OF
VECTOR CALCULUS 85 PROBLEMS 2.1-2.13 92 2.2 LOCAL MAXIMA AND MINIMA,
SIDE CONDITIONS 94 PROBLEMS 2.14-2.21 101 2.3 SECOND-DERIVATIVE TEST 102
PROBLEMS 2.22-2.26 105 2.4 GRADIENT METHOD FOR FINDING CRITICAL POINTS
106 PROBLEMS 2.27-2.28 108 2.5 APPLICATIONS 109 PROBLEMS 2.29-2.33 115
2.6 KARUSH-KUHN-TUCKER CONDITIONS 116 PROBLEMS 2.34-2.37 121 2.7
SUFFICIENT CONDITIONS FOR THE MATHEMATICAL PROGRAMMING PROBLEM 122 2.8
PROOF OF THE KARUSH-KUHN-TUCKER CONDITIONS 127 PROBLEMS 2.38-2.49 130
REFERENCES 134 3 OPTIMIZATION 135 3.1 CONVEXITY 135 PROBLEMS 3.1-3.17
139 3.2 MATHEMATICAL PROGRAMMING, DUALITY 142 3.3 UNCONSTRAINED
QUADRATIC OPTIMIZATION 144 PROBLEMS 3.18-3.28 146 3.4 CONSTRAINED
QUADRATIC OPTIMIZATION IN TZ 148 3.5 QP WITH INEQUALITY CONSTRAINTS, QP
ALGORITHM 153 PROBLEMS 3.29-3.38 156 3.6 LINEAR PROGRAMMING , 158 3.7
SIMPLEX ALGORITHM 166 PROBLEMS 3.39-3.55 173 3.8 LP WITH BOUNDED
VARIABLES 175 PROBLEMS 3.56-3.62 181 3.9 CONVEX FUNCTIONS AND CONVEX
PROGRAMMING 182 PROBLEMS 3.63-3.68 188 3.10 THE FERMAT-WEBER PROBLEM AND
A DUAL PROBLEM 188 PROBLEMS 3.69-3.76 193 3.11 A DUALITY RELATION IN
HIGHER DIMENSIONS 194 PROBLEMS 3.77-3.84 200 REFERENCES 201 4
FENCHEL-ROCKAFELLAR DUALITY THEORY 203 4.1 GENERALIZED DIRECTIONAL
DERIVATIVE 203 CONTENTS VII PROBLEMS 4.1-4.5 205 4.2 LOCAL STRUCTURE OF
THE BOUNDARY OF A CONVEX SET 205 PROBLEMS 4.6-4.8 209 4.3 SUPPORTING
HYPERPLANE, SEPARATING HYPERPLANE 209 PROBLEMS 4.9-4.15 216 4.4 NEW
DEFINITION OF CONVEX FUNCTION, EPIGRAPH, HYPOGRAPH 217 PROBLEMS
4.16-4.17 221 4.5 CONJUGATE OF CONVEX AND CONCAVE FUNCTIONS 221 PROBLEMS
4.18-4.24 227 4.6 FENCHEL DUALITY THEOREM 228 PROBLEMS 4.25-4.32 231 4.7
ROCKAFELLAR DUALITY THEOREM 232 4.8 PROOF OF LEMMA C 238 PROBLEMS
4.33-4.45 240 4.9 NORMS, DUAL NORMS, MINKOWSKI NORMS 242 PROBLEMS
4.46-4.61 250 4.10 GENERALIZED FERMAT-WEBER PROBLEM 252 4.11 APPLICATION
TO FACILITY LOCATION 254 PROBLEMS 4.62-4.74 259 REFERENCES 261 APPENDIX:
LINEAR ALGEBRA 263 ANSWERS TO SELECTED PROBLEMS 271 INDEX 279
|
| any_adam_object | 1 |
| author | Kaplan, Wilfred 1915- |
| author_facet | Kaplan, Wilfred 1915- |
| author_role | aut |
| author_sort | Kaplan, Wilfred 1915- |
| author_variant | w k wk |
| building | Verbundindex |
| bvnumber | BV023775764 |
| callnumber-first | Q - Science |
| callnumber-label | QA306 |
| callnumber-raw | QA306 |
| callnumber-search | QA306 |
| callnumber-sort | QA 3306 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 870 |
| ctrlnum | (OCoLC)38992870 (DE-599)BVBBV023775764 |
| dewey-full | 511/.66 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.66 |
| dewey-search | 511/.66 |
| dewey-sort | 3511 266 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01918nam a2200505zc 4500</leader><controlfield tag="001">BV023775764</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20101029 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">990520s1999 d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0471252891</subfield><subfield code="9">0-471-25289-1</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)38992870</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV023775764</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-634</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA306</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">511/.66</subfield><subfield code="2">21</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="100" ind1="1" ind2=" "><subfield code="a">Kaplan, Wilfred</subfield><subfield code="d">1915-</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Maxima and minima with applications</subfield><subfield code="b">practical optimization and duality</subfield><subfield code="c">Wilfred Kaplan</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York [u.a.]</subfield><subfield code="b">Wiley</subfield><subfield code="c">1999</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">X, 284 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">Wiley-Interscience series in discrete mathematics and optimization</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Análise variacional</subfield><subfield code="2">larpcal</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Maxima</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Minima (natuurwetenschappen)</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Optimaliseren</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Programação convexa</subfield><subfield code="2">larpcal</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical optimization</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Maxima and minima</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Minimum</subfield><subfield code="0">(DE-588)4467521-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Analytische Geometrie</subfield><subfield code="0">(DE-588)4001867-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Maximum</subfield><subfield code="0">(DE-588)4467522-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Optimierung</subfield><subfield code="0">(DE-588)4043664-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Maximum</subfield><subfield code="0">(DE-588)4467522-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Minimum</subfield><subfield code="0">(DE-588)4467521-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Analytische Geometrie</subfield><subfield code="0">(DE-588)4001867-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="3"><subfield code="a">Optimierung</subfield><subfield code="0">(DE-588)4043664-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">GBV 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=017417982&sequence=000001&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:BVB01-017417982</subfield></datafield></record></collection> |
| id | DE-604.BV023775764 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:36:34Z |
| institution | BVB |
| isbn | 0471252891 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017417982 |
| oclc_num | 38992870 |
| open_access_boolean | |
| owner | DE-634 |
| owner_facet | DE-634 |
| physical | X, 284 S. graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley-Interscience series in discrete mathematics and optimization |
| spelling | Kaplan, Wilfred 1915- Verfasser aut Maxima and minima with applications practical optimization and duality Wilfred Kaplan New York [u.a.] Wiley 1999 X, 284 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley-Interscience series in discrete mathematics and optimization Análise variacional larpcal Maxima gtt Minima (natuurwetenschappen) gtt Optimaliseren gtt Programação convexa larpcal Mathematical optimization Maxima and minima Minimum (DE-588)4467521-5 gnd rswk-swf Analytische Geometrie (DE-588)4001867-2 gnd rswk-swf Maximum (DE-588)4467522-7 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Maximum (DE-588)4467522-7 s Minimum (DE-588)4467521-5 s Analytische Geometrie (DE-588)4001867-2 s Optimierung (DE-588)4043664-0 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017417982&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kaplan, Wilfred 1915- Maxima and minima with applications practical optimization and duality Análise variacional larpcal Maxima gtt Minima (natuurwetenschappen) gtt Optimaliseren gtt Programação convexa larpcal Mathematical optimization Maxima and minima Minimum (DE-588)4467521-5 gnd Analytische Geometrie (DE-588)4001867-2 gnd Maximum (DE-588)4467522-7 gnd Optimierung (DE-588)4043664-0 gnd |
| subject_GND | (DE-588)4467521-5 (DE-588)4001867-2 (DE-588)4467522-7 (DE-588)4043664-0 |
| title | Maxima and minima with applications practical optimization and duality |
| title_auth | Maxima and minima with applications practical optimization and duality |
| title_exact_search | Maxima and minima with applications practical optimization and duality |
| title_full | Maxima and minima with applications practical optimization and duality Wilfred Kaplan |
| title_fullStr | Maxima and minima with applications practical optimization and duality Wilfred Kaplan |
| title_full_unstemmed | Maxima and minima with applications practical optimization and duality Wilfred Kaplan |
| title_short | Maxima and minima with applications |
| title_sort | maxima and minima with applications practical optimization and duality |
| title_sub | practical optimization and duality |
| topic | Análise variacional larpcal Maxima gtt Minima (natuurwetenschappen) gtt Optimaliseren gtt Programação convexa larpcal Mathematical optimization Maxima and minima Minimum (DE-588)4467521-5 gnd Analytische Geometrie (DE-588)4001867-2 gnd Maximum (DE-588)4467522-7 gnd Optimierung (DE-588)4043664-0 gnd |
| topic_facet | Análise variacional Maxima Minima (natuurwetenschappen) Optimaliseren Programação convexa Mathematical optimization Maxima and minima Minimum Analytische Geometrie Maximum Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017417982&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kaplanwilfred maximaandminimawithapplicationspracticaloptimizationandduality |