Smooth nonlinear optimization in R n:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer Acad. Publ.
1997
|
| Series: | Nonconvex optimization and its applications
19 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 374 S. graph. Darst. |
| ISBN: | 0792346807 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV011855118 | ||
| 003 | DE-604 | ||
| 005 | 19980331 | ||
| 007 | t | ||
| 008 | 980326s1997 d||| |||| 00||| eng d | ||
| 020 | |a 0792346807 |9 0-7923-4680-7 | ||
| 035 | |a (OCoLC)37211267 | ||
| 035 | |a (DE-599)BVBBV011855118 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-20 |a DE-703 |a DE-29T |a DE-634 |a DE-83 | ||
| 050 | 0 | |a QA402.5 | |
| 082 | 0 | |a 519.7/6 |2 21 | |
| 084 | |a SK 870 |0 (DE-625)143265: |2 rvk | ||
| 084 | |a 90C30 |2 msc | ||
| 084 | |a 65K05 |2 msc | ||
| 100 | 1 | |a Rapcsák, Tamás |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Smooth nonlinear optimization in R n |c by Tamás Rapcsák |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer Acad. Publ. |c 1997 | |
| 300 | |a XIII, 374 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Nonconvex optimization and its applications |v 19 | |
| 650 | 7 | |a Niet-lineaire theorieën |2 gtt | |
| 650 | 7 | |a Optimaliseren |2 gtt | |
| 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 |
| 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 | |
| 689 | 1 | 0 | |a Nichtlineare Optimierung |0 (DE-588)4128192-5 |D s |
| 689 | 1 | |5 DE-604 | |
| 830 | 0 | |a Nonconvex optimization and its applications |v 19 |w (DE-604)BV010085908 |9 19 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008007623&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-008007623 | ||
Record in the Search Index
| _version_ | 1804126440536408064 |
|---|---|
| adam_text | CONTENTS
PREFACE xiii
1 INTRODUCTION 1
2 NONLINEAR OPTIMIZATION PROBLEMS 7
2.1 Historical survey of nonlinear optimization 7
2.2 Classical nonlinear optimization problems and optimality
conditions 12
2.3 Convex optimization 18
2.4 Separation theorems 23
3 OPTIMALITY CONDITIONS 27
3.1 Smooth nonlinear optimization problems 27
3.2 Necessary optimality conditions 29
3.3 Sufficient optimality conditions 34
4 GEOMETRIC BACKGROUND OF
OPTIMALITY CONDITIONS 37
4.1 Geometric meaning of optimality conditions 37
4.2 Classical differential geometric aspects 41
5 DEDUCTION OF THE CLASSICAL
OPTIMALITY CONDITIONS IN
NONLINEAR OPTIMIZATION 45
5.1 First order necessary conditions under equality constraints 45
5.2 Second order conditions under equality constraints 48
vii
viii Smooth Nonlinear Optimization in Rn
5.3 Necessary and sufficient conditions under inequality con¬
straints 51
5.4 A second order sufficient condition 54
6 GEODESIC CONVEX FUNCTIONS 61
6.1 Geodesic convex functions on Riemannian manifolds 63
6.2 First order characterization 72
6.3 Second order characterization 75
6.4 Optimality conditions and geodesic convexity 80
6.5 Geodesic convexity in nonlinear optimization 81
6.6 Concluding remarks 85
7 ON THE CONNECTEDNESS OF
THE SOLUTION SET TO
COMPLEMENTARITY SYSTEMS 87
7.1 Linear complementarity systems 89
7.2 The case of LCS with one parameter 94
7.3 Nonlinear complementarity systems 96
7.4 Generalized nonlinear complementarity systems 101
7.5 Variational inequalities 102
7.6 Image problem 106
7.7 Concluding remarks 108
8 NONLINEAR COORDINATE
REPRESENTATIONS ill
8.1 Formulation of the problem 112
8.2 Nonlinear coordinate representations in Rn 114
8.3 Right inverses and projections 117
8.4 Inverse of partitioned matrices by right inverses 127
8.5 Nonlinear coordinate representations in constrained opti¬
mization 130
8.6 Nonlinear coordinate representations of Riemannian metrics 133
8.7 Convexification by nonlinear coordinate transformations 135
8.8 Image representations 135
8.9 Concluding remarks 139
Contents ix
9 TENSORS IN OPTIMIZATION 141
9.1 Tensors 142
9.2 Tensors in coordinate representations 145
9.3 Smooth unconstrained optimization problems 148
9.4 Improvement of the structure of global optimization prob¬
lems 153
9.5 Smooth constrained optimization problems 157
9.6 Tensor approximations of smooth functions on Riemannian
manifolds 160
9.7 Tensor field complementarity systems 162
9.8 Concluding remarks 165
10 GEODESIC CONVEXITY ON B^ 167
10.1 Geodesic convexity with respect to the affine metric 169
10.2 Geodesic convexity with respect to other Riemannian met¬
rics 177
10.3 Geodesic convexity of separable functions 180
11 VARIABLE METRIC METHODS ALONG
GEODESICS 185
11.1 General framework for variable metric methods on Rieman¬
nian submanifolds in Rn 186
11.2 Convergence of variable metric methods along geodesies 190
11.3 Rate of convergence for variable metric methods along geo¬
desies 196
11.4 Variable metric methods along geodesies under inequality
constraints 200
11.5 An optimization approach for solving smooth nonlinear com¬
plementarity systems 204
12 POLYNOMIAL VARIABLE METRIC
METHODS FOR LINEAR
OPTIMIZATION 207
12.1 A class of polynomial variable metric algorithms for linear
optimization 210
12.2 Riemannian metric for the affine scaling vector field 223
12.3 Riemannian metric for the projective scaling vector field 226
x Smooth Nonlinear Optimization in Rn
13 SPECIAL FUNCTION CLASSES 231
13.1 Geodesic quasiconvex functions 231
13.2 Geodesic pseudoconvex functions 233
13.3 Difference of two geodesic convex functions 235
13.4 Convex transformable functions 236
13.5 Pseudolinear functions 239
14 FENCHEL S UNSOLVED PROBLEM OF
LEVEL SETS 253
14.1 Fenchel problem of level sets 255
14.2 Preference orderings 257
14.3 Utility functions of a preference ordering 258
14.4 Main results 262
14.5 Preliminary Lemmas and Theorems 267
14.6 Proof of Theorems 14.4.1, 14.4.1 269
14.7 Proof of Theorem 14.4.2 270
15 AN IMPROVEMENT OF THE LAGRANGE
MULTIPLIER RULE FOR SMOOTH
OPTIMIZATION PROBLEMS 271
15.1 Lagrange multiplier rule for the case of equality constraints 272
15.2 Improved Lagrange multiplier rule for the case of equality
constraints . 274
15.3 Improved Lagrange multiplier rule for the case of equality
and inequality constraints 280
15.4 Some chances of application 283
A ON THE CONNECTION BETWEEN
MECHANICAL FORCE EQUILIBRIUM
AND NONLINEAR OPTIMIZATION 285
A.I Statement of the mechanical force equilibrium problem 286
A.2 Characterization of the constraints 287
A.3 Characterization of a force equilibrium point by the Court
ivron principle 289
A.4 Characterization of a force equilibrium point by the princi¬
ple of virtual work 290
Contents xi
A.5 Relation between the principle of virtual work and the Court
ivron principle 293
A.6 Possible velocities in the case of time dependent constraints 293
A.7 Relation between the principle of virtual work and the Courtiv
ron principle in the case of time dependent constraints 301
A.8 Equations of motions by force equilibrium 303
B TOPOLOGY 305
B.I Topological spaces 305
B.2 Metric spaces 312
B.3 Continuous mappings and homeomorphisms 315
B.4 Subspaces and product spaces 318
B.5 Compactness 321
B.6 Connectedness 325
C RIEMANNIAN GEOMETRY 329
C.I From the history of differential geometry 329
C.2 Riemannian manifolds 331
C.3 Geodesic convex functions 336
C.4 Riemannian manifolds in Euclidean spaces 338
REFERENCES 341
AUTHOR INDEX 363
SUBJECT INDEX 367
NOTATIONS 373
|
| any_adam_object | 1 |
| author | Rapcsák, Tamás |
| author_facet | Rapcsák, Tamás |
| author_role | aut |
| author_sort | Rapcsák, Tamás |
| author_variant | t r tr |
| building | Verbundindex |
| bvnumber | BV011855118 |
| 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 | SK 870 |
| ctrlnum | (OCoLC)37211267 (DE-599)BVBBV011855118 |
| 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 |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01775nam a2200469 cb4500</leader><controlfield tag="001">BV011855118</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">19980331 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">980326s1997 d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0792346807</subfield><subfield code="9">0-7923-4680-7</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)37211267</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV011855118</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="049" ind1=" " ind2=" "><subfield code="a">DE-20</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-83</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">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="084" ind1=" " ind2=" "><subfield code="a">90C30</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="100" ind1="1" ind2=" "><subfield code="a">Rapcsák, Tamás</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Smooth nonlinear optimization in R n</subfield><subfield code="c">by Tamás Rapcsák</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Dordrecht [u.a.]</subfield><subfield code="b">Kluwer Acad. Publ.</subfield><subfield code="c">1997</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIII, 374 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="1" ind2=" "><subfield code="a">Nonconvex optimization and its applications</subfield><subfield code="v">19</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Niet-lineaire theorieën</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="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="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="689" ind1="1" 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="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Nonconvex optimization and its applications</subfield><subfield code="v">19</subfield><subfield code="w">(DE-604)BV010085908</subfield><subfield code="9">19</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ 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=008007623&sequence=000002&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:BVB01-008007623</subfield></datafield></record></collection> |
| id | DE-604.BV011855118 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:17:29Z |
| institution | BVB |
| isbn | 0792346807 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008007623 |
| oclc_num | 37211267 |
| open_access_boolean | |
| owner | DE-20 DE-703 DE-29T DE-634 DE-83 |
| owner_facet | DE-20 DE-703 DE-29T DE-634 DE-83 |
| physical | XIII, 374 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series | Nonconvex optimization and its applications |
| series2 | Nonconvex optimization and its applications |
| spelling | Rapcsák, Tamás Verfasser aut Smooth nonlinear optimization in R n by Tamás Rapcsák Dordrecht [u.a.] Kluwer Acad. Publ. 1997 XIII, 374 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Nonconvex optimization and its applications 19 Niet-lineaire theorieën gtt Optimaliseren gtt Mathematical optimization Nonlinear theories Nichtlineare Optimierung (DE-588)4128192-5 gnd rswk-swf Lineare Optimierung (DE-588)4035816-1 gnd rswk-swf Lineare Optimierung (DE-588)4035816-1 s DE-604 Nichtlineare Optimierung (DE-588)4128192-5 s Nonconvex optimization and its applications 19 (DE-604)BV010085908 19 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008007623&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rapcsák, Tamás Smooth nonlinear optimization in R n Nonconvex optimization and its applications Niet-lineaire theorieën gtt Optimaliseren gtt Mathematical optimization Nonlinear theories Nichtlineare Optimierung (DE-588)4128192-5 gnd Lineare Optimierung (DE-588)4035816-1 gnd |
| subject_GND | (DE-588)4128192-5 (DE-588)4035816-1 |
| title | Smooth nonlinear optimization in R n |
| title_auth | Smooth nonlinear optimization in R n |
| title_exact_search | Smooth nonlinear optimization in R n |
| title_full | Smooth nonlinear optimization in R n by Tamás Rapcsák |
| title_fullStr | Smooth nonlinear optimization in R n by Tamás Rapcsák |
| title_full_unstemmed | Smooth nonlinear optimization in R n by Tamás Rapcsák |
| title_short | Smooth nonlinear optimization in R n |
| title_sort | smooth nonlinear optimization in r n |
| topic | Niet-lineaire theorieën gtt Optimaliseren gtt Mathematical optimization Nonlinear theories Nichtlineare Optimierung (DE-588)4128192-5 gnd Lineare Optimierung (DE-588)4035816-1 gnd |
| topic_facet | Niet-lineaire theorieën Optimaliseren Mathematical optimization Nonlinear theories Nichtlineare Optimierung Lineare Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008007623&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV010085908 |
| work_keys_str_mv | AT rapcsaktamas smoothnonlinearoptimizationinrn |