Nonlinear optimization: lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 1 - 7, 2007
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| Other Authors: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin
Springer [u.a.]
2010
|
| Series: | Lecture notes in mathematics
1989 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 279 S. graph. Darst. |
| ISBN: | 9783642113383 |
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MARC
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Record in the Search Index
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| adam_text | 1.3 SET-VALUED TOOLS 08 CONTENTS GLOBAL OPTIMIZATION: A QUADRATIC
PROGRAMMING PERSPECTIVE 1 IMMANUEL M. BOMZE 1 GLOBAL OPTIMIZATION OF
SIMPLEST STRUCTURE: QUADRATIC OPTIMIZATION 3 1.1 LOCAL OPTIMALITY
CONDITIONS IN QPS 4 1.2 EXTREMAL INCREMENTS AND GLOBAL OPTIMALITY 6 1.3
GLOBAL OPTIMALITY AND E-SUBDIFFERENTIAL CALCULUS 9 1.4 LOCAL OPTIMALITY
AND E-SUBDIFFERENTIAL CALCULUS 11 1.5 S-SUBDIFFERENTIAL OPTIMALITY
CONDITIONS IN QPS 15 1.6 STANDARD QUADRATIC PROBLEMS (STQPS) 21 1.7 SOME
APPLICATIONS OF STQPS 23 2 SOME BASIC TECHNIQUES, ILLUSTRATED BY STQPS
25 2.1 LOCAL SEARCH AND ESCAPE DIRECTIONS 2FI 2.2 BOUNDING AND ADDITIVE
DECOMPOSITIONS 29 2.3 BRANCH-AND-BOUND: PRINCIPLES AND SPECIAL CASES 32
3 REFORMULATION, RELAXATION, APPROXIMATION 33 3.1 QUARTIC AND
UNCONSTRAINED REFORMULATIONS 34 3.2 CONVEX CONIC REFORMULATIONS 35 3.3
COPOSITIVE PROGRAMMING 37 4 APPROACHES TO COPOSITIVITY 41 4.1
COPOSITIVITY DETECTION 41 4.2 APPROXIMATION HIERARCHIES 4(I 4.3
COMPLEXITY ISSUES 48 4.4 SDP RELAXATION BOUNDS FOR STQPS. REVISITED 49
REFERENCES 50 NONSMOOTH OPTIMIZATION 55 VLADIMIR F. DEMYANOV 1
INTRODUCTION 55 1.1 THE SMOOTH CASE: THE KINGDOM OF GRADIENT 00 1.2 IN
THE SEARCH FOR A SUCCESSOR 02 BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/99858925X DIGITALISIERT DURCH X CONTENTS 1.4 THE
APPROXIMATION OF THE DIRECTIONAL DERIVATIVE BY A FAMILY OF CONVEX
FUNCTIONS: QUASIDIFFERENTIABLE FUNCTIONS 73 2 UNCONSTRAINED OPTIMIZATION
PROBLEMS 84 2.1 OPTIMIZATION IN A METRIC SPACE 84 2.2 OPTIMIZATION IN A
NORMED SPACE 93 2.3 DIRECTIONAL DIFFERENTIABILITY IN A NORMED SPACE 100
2.4 THE GATEAUX AND FRECHET DIFFERENTIABILITY 103 2.5 THE
FINITE-DIMENSIONAL CASE 106 3 CONSTRAINED OPTIMIZATION PROBLEMS VIA
EXACT PENALIZATION 116 3.1 OPTIMIZATION IN A METRIC SPACE IN THE
PRESENCE OF CONSTRAINTS 117 3.2 THE CONSTRAINED OPTIMIZATION PROBLEM IN
A NORMED SPACE 119 3.3 PENALTY FUNCTIONS 122 3.4 EXACT PENALTY FUNCTIONS
AND A GLOBAL MINIMUM 129 3.5 EXACT PENALTY FUNCTIONS AND LOCAL MINIMA
132 3.6 EXACT PENALTY FUNCTIONS AND STATIONARY POINTS 139 3.7 EXACT
PENALTY FUNCTIONS AND MINIMIZING SEQUENCES 145 3.8 EXACT SMOOTH PENALTY
FUNCTIONS 150 3.9 MINIMIZATION IN THE FINITE-DIMENSIONAL SPACE 151
REFERENCES 159 THE SEQUENTIAL QUADRATIC PROGRAMMING METHOD 165 ROGER
FLETCHER 1 INTRODUCTION 165 2 NEWTON METHODS AND LOCAL OPTIMALITY 167
2.1 SYSTEMS OF N SIMULTANEOUS EQUATIONS IN N UNKNOWNS 167 2.2 LOCAL
CONVERGENCE OF THE NEWTON-RAPHSON METHOD 168 2.3 UNCONSTRAINED
OPTIMIZATION 170 2.4 OPTIMIZATION WITH LINEAR EQUALITY CONSTRAINTS 171 3
CONTENTS XI 5.4 THE LI EXACT PENALTY FUNCTION 194 5.5 SQP WITH THE /JEPF
196 6 FILTER METHODS 197 6.1 SQP FILTER METHODS 199 6.2 A FILTER
CONVERGENCE PROOF 200 6.3 OTHER FILTER SQP METHODS 203 7 MODELLING
LANGUAGES AND NEOS 204 7.1 THE AMPL LANGUAGE 204 7.2 NETWORKS IN AMPL
206 7.3 OTHER USEFUL AMPL FEATURES 208 7.4 ACCESSING AMPL 210 7.5 NEOS
AND KESTREL 210 REFERENCES 212 INTERIOR POINT METHODS FOR NONLINEAR
OPTIMIZATION 215 IMRE POLIK AND TAMAS TERLAKY 1 INTRODUCTION 215 1.1
HISTORICAL BACKGROUND 215 1.2 NOTATION AND PRELIMINARIES 216 2 INTERIOR
POINT METHODS FOR LINEAR OPTIMIZATION 218 2.1 THE LINEAR OPTIMIZATION
PROBLEM 218 2.2 THE SKEW-SYMMETRIC SELF-DUAL MODEL 222 2.3 SUMMARY OF
THE THEORETICAL RESULTS 237 2.4 A GENERAL SCHEME OF IP ALGORITHMS FOR
LINEAR OPTIMIZATION... 239 2.5 *THE BARRIER APPROACH 244 3 INTERIOR
POINT METHODS FOR CONIC OPTIMIZATION 245 3.1 PROBLEM DESCRIPTION 245 3.2
APPLICATIONS OF CONIC OPTIMIZATION 248 3.3 INITIALIZATION BY EMBEDDING
249 3.4 CONIC OPTIMIZATION AS A COMPLEMENTARITY PROBLEM 250 3.5 SUMMARY
260 3.6 *BARRIER FUNCTIONS IN CONIC OPTIMIZATION 261 4 INTERIOR POINT
METHODS FOR NONLINEAR OPTIMIZATION 262 4.1 NONLINEAR OPTIMIZATION AS A
COMPLEMENTARITY PROBLEM 262 4.2 INTERIOR POINT METHODS FOR NONLINEAR
COMPLEMENTARIT XII CONTENTS 6.3 SPECIAL STRUCTURES 270 6.4 WARMSTARTING
270 6.5 PARALLELIZATION 271 REFERENCES 271 LIST OF PARTICIPANTS 277
|
| any_adam_object | 1 |
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| callnumber-first | Q - Science |
| callnumber-label | QA3 |
| callnumber-raw | QA3 QA402.5 |
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| dewey-full | 519.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.3 |
| dewey-search | 519.3 |
| dewey-sort | 3519.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| language | English |
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| physical | XII, 279 S. graph. Darst. |
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| series | Lecture notes in mathematics |
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| spelling | Nonlinear optimization lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 1 - 7, 2007 Immanuel M. Bomze ... Ed.: Gianni Di Pillo ... Berlin Springer [u.a.] 2010 XII, 279 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1989 Mathematical optimization Congresses Nonlinear theories Congresses Nichtlineare Optimierung (DE-588)4128192-5 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2007 Cetraro gnd-content Nichtlineare Optimierung (DE-588)4128192-5 s DE-604 Bomze, Immanuel M. 1958- Sonstige (DE-588)110173023 oth Di Pillo, Gianni (DE-588)140931139 edt Centro Internazionale Matematico Estivo Sonstige (DE-588)1025933-8 oth Lecture notes in mathematics 1989 (DE-604)BV000676446 1989 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020195272&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nonlinear optimization lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 1 - 7, 2007 Lecture notes in mathematics Mathematical optimization Congresses Nonlinear theories Congresses Nichtlineare Optimierung (DE-588)4128192-5 gnd |
| subject_GND | (DE-588)4128192-5 (DE-588)1071861417 |
| title | Nonlinear optimization lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 1 - 7, 2007 |
| title_auth | Nonlinear optimization lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 1 - 7, 2007 |
| title_exact_search | Nonlinear optimization lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 1 - 7, 2007 |
| title_full | Nonlinear optimization lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 1 - 7, 2007 Immanuel M. Bomze ... Ed.: Gianni Di Pillo ... |
| title_fullStr | Nonlinear optimization lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 1 - 7, 2007 Immanuel M. Bomze ... Ed.: Gianni Di Pillo ... |
| title_full_unstemmed | Nonlinear optimization lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 1 - 7, 2007 Immanuel M. Bomze ... Ed.: Gianni Di Pillo ... |
| title_short | Nonlinear optimization |
| title_sort | nonlinear optimization lectures given at the c i m e summer school held in cetraro italy july 1 7 2007 |
| title_sub | lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 1 - 7, 2007 |
| topic | Mathematical optimization Congresses Nonlinear theories Congresses Nichtlineare Optimierung (DE-588)4128192-5 gnd |
| topic_facet | Mathematical optimization Congresses Nonlinear theories Congresses Nichtlineare Optimierung Konferenzschrift 2007 Cetraro |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020195272&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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