Introduction to the theory of nonlinear optimization:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
Springer
1994
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 249 S. graph. Darst. |
| ISBN: | 3540583203 0387583203 |
Staff View
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV009780044 | ||
| 003 | DE-604 | ||
| 005 | 20100629 | ||
| 007 | t | ||
| 008 | 940822s1994 gw d||| |||| 00||| eng d | ||
| 016 | 7 | |a 941900118 |2 DE-101 | |
| 020 | |a 3540583203 |9 3-540-58320-3 | ||
| 020 | |a 0387583203 |9 0-387-58320-3 | ||
| 035 | |a (OCoLC)31044770 | ||
| 035 | |a (DE-599)BVBBV009780044 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-384 |a DE-703 |a DE-M347 |a DE-739 |a DE-12 |a DE-824 |a DE-91 |a DE-91G |a DE-473 |a DE-29T |a DE-706 |a DE-634 |a DE-83 |a DE-11 |a DE-188 | ||
| 050 | 0 | |a QA402.5 | |
| 082 | 0 | |a 519.7/6 |2 20 | |
| 084 | |a QH 425 |0 (DE-625)141579: |2 rvk | ||
| 084 | |a SK 870 |0 (DE-625)143265: |2 rvk | ||
| 084 | |a SK 890 |0 (DE-625)143267: |2 rvk | ||
| 084 | |a MAT 916f |2 stub | ||
| 084 | |a 49J27 |2 msc | ||
| 100 | 1 | |a Jahn, Johannes |d 1951- |e Verfasser |0 (DE-588)104274905 |4 aut | |
| 245 | 1 | 0 | |a Introduction to the theory of nonlinear optimization |c Johannes Jahn |
| 264 | 1 | |a Berlin u.a. |b Springer |c 1994 | |
| 300 | |a VIII, 249 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Optimaliseren |2 gtt | |
| 650 | 7 | |a Optimisation mathématique |2 ram | |
| 650 | 7 | |a Théories non-linéaires |2 ram | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 4 | |a Nonlinear theories | |
| 650 | 0 | 7 | |a Nichtlineare Optimierung |0 (DE-588)4128192-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nichtlineare Optimierung |0 (DE-588)4128192-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006471643&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-006471643 | ||
Record in the Search Index
| _version_ | 1804124129877557248 |
|---|---|
| adam_text | JOHANNES JAHN
INTRODUCTION
TO THE THEORY
OF NONLINEAR
OPTIMIZATION
WITH 30 FIGURES
SPRINGER-VERLAG
BERLIN HEIDELBERG NEW YORK
LONDON PARIS TOKYO
HONG KONG BARCELONA
BUDAPEST
CONTENTS
PREFACE V
1 INTRODUCTION AND PROBLEM FORMULATION 1
2 EXISTENCE THEOREMS FOR MINIMAL POINTS 7
2.1 PROBLEM FORMULATION 7
2.2 EXISTENCE THEOREMS 8
2.3 SET OF MINIMAL POINTS 18
2.4 APPLICATION ** APPROXIMATION PROBLEMS 19
2.5 APPLICATION TO OPTIMAL CONTROL PROBLEMS 24
EXERCISES 30
3 GENERALIZED DERIVATIVES 33
3.1 DIRECTIONAL DERIVATIVE 33
3.2 GATEAUX AND FRECHET DERIVATIVES 39
3.3 SUBDIFFERENTIAL 51
3.4 QUASIDIFFERENTIAL 59
3.5 CLARKE DERIVATIVE 69
EXERCISES 77
4 TANGENT CONES 81
4.1 DEFINITION AND PROPERTIES 81
4.2 OPTIMALITY CONDITIONS 91
4.3 A LYUSTERNIK THEOREM 98
EXERCISES 106
5 GENERALIZED LAGRANGE MULTIPLIER RULE 109
5.1 PROBLEM FORMULATION 109
VIII CONTENTS
5.2 NECESSARY OPTIMALITY CONDITIONS 112
5.3 SUFFICIENT OPTIMALITY CONDITIONS 130
5.4 APPLICATION TO OPTIMAL CONTROL PROBLEMS 140
EXERCISES 159
6 DUALITY 163
6.1 PROBLEM FORMULATION 163
6.2 DUALITY THEOREMS 168
6.3 SADDLE POINT THEOREMS 172
6.4 LINEAR PROBLEMS 176
6.5 APPLICATION TO APPROXIMATION PROBLEMS 179
EXERCISES 188
7 DIRECT TREATMENT OF SPECIAL OPTIMIZATION PROBLEMS 191
7.1 LINEAR QUADRATIC OPTIMAL CONTROL PROBLEMS 191
7.2 TIME MINIMAL CONTROL PROBLEMS 199
EXERCISES 216
A WEAK CONVERGENCE 219
8 REFLEXIVITY OF BANACH SPACES 221
* HAHN-BANACH THEOREM 223
D PARTIALLY ORDERED LINEAR SPACES 227
BIBLIOGRAPHY 231
INDEX 247
|
| any_adam_object | 1 |
| author | Jahn, Johannes 1951- |
| author_GND | (DE-588)104274905 |
| author_facet | Jahn, Johannes 1951- |
| author_role | aut |
| author_sort | Jahn, Johannes 1951- |
| author_variant | j j jj |
| building | Verbundindex |
| bvnumber | BV009780044 |
| callnumber-first | Q - Science |
| callnumber-label | QA402 |
| callnumber-raw | QA402.5 |
| callnumber-search | QA402.5 |
| callnumber-sort | QA 3402.5 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 425 SK 870 SK 890 |
| classification_tum | MAT 916f |
| ctrlnum | (OCoLC)31044770 (DE-599)BVBBV009780044 |
| dewey-full | 519.7/6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.7/6 |
| dewey-search | 519.7/6 |
| dewey-sort | 3519.7 16 |
| 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>01811nam a2200481 c 4500</leader><controlfield tag="001">BV009780044</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20100629 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">940822s1994 gw d||| |||| 00||| eng d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">941900118</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3540583203</subfield><subfield code="9">3-540-58320-3</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0387583203</subfield><subfield code="9">0-387-58320-3</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)31044770</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV009780044</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-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-M347</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-12</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-473</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-706</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">QA402.5</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.7/6</subfield><subfield code="2">20</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">QH 425</subfield><subfield code="0">(DE-625)141579:</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">SK 890</subfield><subfield code="0">(DE-625)143267:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 916f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">49J27</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Jahn, Johannes</subfield><subfield code="d">1951-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)104274905</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Introduction to the theory of nonlinear optimization</subfield><subfield code="c">Johannes Jahn</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin u.a.</subfield><subfield code="b">Springer</subfield><subfield code="c">1994</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">VIII, 249 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="650" ind1=" " ind2="7"><subfield code="a">Optimaliseren</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Optimisation mathématique</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Théories non-linéaires</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical optimization</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Nonlinear theories</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Nichtlineare Optimierung</subfield><subfield code="0">(DE-588)4128192-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Nichtlineare Optimierung</subfield><subfield code="0">(DE-588)4128192-5</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">DNB 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=006471643&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:BVB01-006471643</subfield></datafield></record></collection> |
| id | DE-604.BV009780044 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:40:46Z |
| institution | BVB |
| isbn | 3540583203 0387583203 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006471643 |
| oclc_num | 31044770 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-M347 DE-739 DE-12 DE-824 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-473 DE-BY-UBG DE-29T DE-706 DE-634 DE-83 DE-11 DE-188 |
| owner_facet | DE-384 DE-703 DE-M347 DE-739 DE-12 DE-824 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-473 DE-BY-UBG DE-29T DE-706 DE-634 DE-83 DE-11 DE-188 |
| physical | VIII, 249 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Springer |
| record_format | marc |
| spelling | Jahn, Johannes 1951- Verfasser (DE-588)104274905 aut Introduction to the theory of nonlinear optimization Johannes Jahn Berlin u.a. Springer 1994 VIII, 249 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Optimaliseren gtt Optimisation mathématique ram Théories non-linéaires ram Mathematical optimization Nonlinear theories Nichtlineare Optimierung (DE-588)4128192-5 gnd rswk-swf Nichtlineare Optimierung (DE-588)4128192-5 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006471643&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jahn, Johannes 1951- Introduction to the theory of nonlinear optimization Optimaliseren gtt Optimisation mathématique ram Théories non-linéaires ram Mathematical optimization Nonlinear theories Nichtlineare Optimierung (DE-588)4128192-5 gnd |
| subject_GND | (DE-588)4128192-5 |
| title | Introduction to the theory of nonlinear optimization |
| title_auth | Introduction to the theory of nonlinear optimization |
| title_exact_search | Introduction to the theory of nonlinear optimization |
| title_full | Introduction to the theory of nonlinear optimization Johannes Jahn |
| title_fullStr | Introduction to the theory of nonlinear optimization Johannes Jahn |
| title_full_unstemmed | Introduction to the theory of nonlinear optimization Johannes Jahn |
| title_short | Introduction to the theory of nonlinear optimization |
| title_sort | introduction to the theory of nonlinear optimization |
| topic | Optimaliseren gtt Optimisation mathématique ram Théories non-linéaires ram Mathematical optimization Nonlinear theories Nichtlineare Optimierung (DE-588)4128192-5 gnd |
| topic_facet | Optimaliseren Optimisation mathématique Théories non-linéaires Mathematical optimization Nonlinear theories Nichtlineare Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006471643&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT jahnjohannes introductiontothetheoryofnonlinearoptimization |