Solution methods for bilevel programming problems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | German |
| Published: |
München
Dr. Hut Verlag
2009
|
| Edition: | 1. Aufl. |
| Series: | Mathematik
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | III, 122 S. graph. Darst. |
| ISBN: | 9783899639315 |
Staff View
MARC
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Record in the Search Index
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| adam_text | CONTENTS 1 INTRODUCTION 1 2 PRELIMINARIES 7 2.1 POSITIVE DEFINITE MATRIX
7 2.2 CONVEX SET 8 2.2.1 CONES 9 2.2.2 EXTREME POINT 10 2.3 CONVEX
FUNCTION 10 2.4 LOWER AND UPPER SEMI-CONTINUITY OF A FUNCTION 11 2.5
LIPSCHITZ CONTINUITY 12 2.6 THE DIRECTIONAL DERIVATIVE 13 2.6.1
CLASSICAL DIRECTIONAL DERIVATIVE 13 2.6.2 GENERALIZED DIRECTIONAL
DERIVATIVE 14 2.6.3 THE CLARKE GENERALIZED GRADIENT 15 2.7 SET VALUED
MAP 15 2.8 UNCONSTRAINED OPTIMIZATION 16 2.9 CONSTRAINED OPTIMIZATION
PROBLEMS 18 2.9.1 PROBLEM FORMULATION 18 2.9.2 CONSTRAINT QUALIFICATION
19 2.9.3 OPTIMALITY CONDITION 21 2.10 FEASIBLE DIRECTION METHOD 23 2.11
NONDIFFERENTIABLE NONLINEAR OPTIMIZATION PROBLEMS 25 III BIBLIOGRAFISCHE
INFORMATIONEN HTTP://D-NB.INFO/99264495X DIGITALISIERT DURCH 6
RELAXATION AND FEASIBLE DIRECTION METHOD 91 3 LINEAR BILEVEL PROGRAMMING
29 3.1 PROBLEM FORMULATION 29 3.2 EXISTENCE OF A SOLUTION FOR THE
OPTIMISTIC APPROACH 32 3.3 OPTIMALITY CONDITIONS 34 3.4 THE EFFECT OF
SHIFTING CONSTRAINTS 41 3.5 THE PESSIMISTIC APPROACH 43 4 NONLINEAR
BILEVEL PROGRAMMING 45 4.1 INTRODUCTION 45 4.2 THE LOWER LEVEL PROBLEM
47 4.2.1 UPPER AND LOWER SEMI-CONTINUITY OF SOLUTION SET MAP- PING 48
4.2.2 OPTIMALITY CONDITION FOR THE LOWER LEVEL PROBLEM . . 49 4.2.3
PROPERTIES OF THE SOLUTION FUNCTION 50 4.2.4 PIECEWISE CONTINUOUSLY
DIFFERENTIABLE FUNCTIONS ... 53 4.3 PESSIMISTIC BILEVEL PROGRAMMING 54
4.4 OPTIMISTIC BILEVEL PROGRAMMING 55 4.5 OPTIMALITY CONDITIONS 56 4.5.1
OPTIMALITY CONDITION BASED ON KKT REFORMULATION 56 4.5.2 OPTIMALITY
CONDITION BASED ON STRONG STABILITY . . 62 4.5.3 OPTIMALITY CONDITION
BASED ON OPTIMAL VALUE FUNCTION 63 5 DIRECT SEARCH METHODS FOR BILEVEL
PROGRAMMING 69 5.1 INTRODUCTION 69 5.2 APPLICABILITY OF DIRECT SEARCH
METHODS 70 5.3 COORDINATE SEARCH 71 5.4 GENERALIZATION OF COORDINATE
SEARCH 74 5.5 COMPONENTS OF PROVING GLOBAL CONVERGENCE 77 5.6
APPLICATION TO BILEVEL PROGRAMMING 78 INDEX 123 6.1 INTRODUCTION 91 6.2
OPTIMALITY 92 6.3 NUMERICAL EXPERIENCE 107 6.3.1 RELAXATION METHOD 108
6.3.2 FEASIBLE DIRECTION METHOD 109 B IBLIOGR APHY 111
|
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| author | Ayalew Getachew Mersha 1973- |
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| dewey-full | 519.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.6 |
| dewey-search | 519.6 |
| dewey-sort | 3519.6 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. Aufl. |
| format | Thesis Book |
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| indexdate | 2024-07-09T21:31:30Z |
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| isbn | 9783899639315 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017138165 |
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| physical | III, 122 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
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| publisher | Dr. Hut Verlag |
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| series2 | Mathematik |
| spelling | Ayalew Getachew Mersha 1973- Verfasser (DE-588)130824577 aut Solution methods for bilevel programming problems Ayalew Getachew Mersha 1. Aufl. München Dr. Hut Verlag 2009 III, 122 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematik Zugl.: Freiberg (Sachsen), Techn. Univ., Diss., 2008 Zwei-Ebenen-Optimierung Zwei-Ebenen-Optimierung (DE-588)4715689-2 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Zwei-Ebenen-Optimierung (DE-588)4715689-2 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017138165&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ayalew Getachew Mersha 1973- Solution methods for bilevel programming problems Zwei-Ebenen-Optimierung Zwei-Ebenen-Optimierung (DE-588)4715689-2 gnd |
| subject_GND | (DE-588)4715689-2 (DE-588)4113937-9 |
| title | Solution methods for bilevel programming problems |
| title_auth | Solution methods for bilevel programming problems |
| title_exact_search | Solution methods for bilevel programming problems |
| title_full | Solution methods for bilevel programming problems Ayalew Getachew Mersha |
| title_fullStr | Solution methods for bilevel programming problems Ayalew Getachew Mersha |
| title_full_unstemmed | Solution methods for bilevel programming problems Ayalew Getachew Mersha |
| title_short | Solution methods for bilevel programming problems |
| title_sort | solution methods for bilevel programming problems |
| topic | Zwei-Ebenen-Optimierung Zwei-Ebenen-Optimierung (DE-588)4715689-2 gnd |
| topic_facet | Zwei-Ebenen-Optimierung Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017138165&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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