Mathematical programs with equilibrium constraints:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2008
|
| Edition: | digitally print. vers. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXIV, 401 S. |
| ISBN: | 9780521065085 |
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MARC
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| 100 | 1 | |a Luo, Zhi-Quan |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Mathematical programs with equilibrium constraints |c Zhi-Quan Luo ; Jong-Shi Pang ; Daniel Ralph |
| 250 | |a digitally print. vers. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2008 | |
| 300 | |a XXIV, 401 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Programming (Mathematics) | |
| 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 |
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| 700 | 1 | |a Pang, Jong-Shi |e Verfasser |4 aut | |
| 700 | 1 | |a Ralph, Daniel |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017103235&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-017103235 | ||
Record in the Search Index
| _version_ | 1804138597522079744 |
|---|---|
| adam_text | Contents
Numbering
System xi
Acronyms
xiii
Glossary of Notation
xv
Preface
xxi
1
Introduction
1
1.1
Problem Formulation
...................... 1
1.2
Source Problems
......................... 9
1.3
Equivalent Constraint Formulations
.............. 34
1.3.1
MPEC in normal form
................. 35
1.3.2
MPEC in KKT form
.................. 38
1.3.3
Merit functions for CP/VI
............... 51
1.3.4
Monotonicity and the implicit form
.......... 54
1.4
Existence of Optimal Solutions
................ 57
2
Exact Penalization of MPEC
61
2.1
General Exact Penalty Results
................. 63
2.2
Penalty Results for MPEC
................... 70
2.3
Improved Error Bounds
..................... 74
2.3.1
Hoffman s error bound for linear systems
....... 78
2.3.2
Error bounds for AVI and LCP
............ 81
2.3.3
Error bounds for a quadratic system
......... 87
2.3.4
Error bounds for NCP
................. 95
2.4
Improved Penalty Results for MPEC
............. 102
vii
viii Contents
2.4.1
AVI
constrained mathematical program
........ 102
2.4.2
NCP constrained mathematical program
....... 108
2.4.3
Optimality conditions: preliminary discussion
.... 109
3
First-Order Optimality Conditions
113
3.1
Elementary. Stationarity Concepts
............... 114
3.2
The Tangent Cone
....................... 118
3.3
Stationarity Under the Pull CQ for MPEC
.......... 126
3.3.1
Primal-dual characterization of stationarity
...... 129
3.4
More About the KKT Formulation of MPEC
........ 137
4
Verification of MPEC Hypotheses
145
4.1
AVI Constrained Mathematical Program
........... 146
4.2
An Implicit Programming Approach
............. 151
4.2.1
B-differentiable functions
................ 154
4.2.2
Key implicit assumption
................ 157
4.2.3
Piecewise smooth functions and degree theory
.... 159
4.2.4
Existence of a piecewise smooth implicit function
. . 172
4.2.5
Calculation of directional derivatives
......... 186
4.2.6
Verification of CQs for MPEC
............. 193
4.2.7
More on strong coherent orientation
.......... 196
4.3
A Piecewise Programming Approach
............. 206
4.3.1
Uniqueness of MPEC multipliers
............ 213
4.4
An Exact Penalty Equivalent of Order
1........... 219
5
Second-Order Optimality Conditions
223
5.1
Review of Second-Order NLP Optimality Theory
...... 224
5.2
AVI Constrained Mathematical Program
........... 227
5.3
NCP Constrained Mathematical Program
.......... 233
5.4
Implicit Programming Based Results
............. 242
5.5
KKT Constrained Mathematical Program
.......... 254
5.6
A Piecewise Programming Approach
............. 258
5.6.1
Sufficiency based on the relaxed NLP
......... 265
6
Algorithms for MPEC
271
6.1
A Penalty Interior Point Algorithm
.............. 272
6.1.1
Optimality conditions
..................273
Contents ix
6.1.2
Preliminaries for
PIPA
................. 277
6.1.3
Algorithm description and convergence analysis
. . . 288
6.1.4
Special cases
....................... 300
6.2
An Alternative
PIPA
for LCP Constrained MP
....... 312
6.3
An Implicit Programming Based Algorithm
......... 320
6.3.1
Algorithm description and convergence
........ 321
6.3.2
Implementation issues
.................. 329
6.4
A Piecewise SQP Approach
.................. 331
6.4.1
A brief review of SQP methods for NLP
....... 331
6.4.2
A PSQP method for MPEC
.............. 336
6.5
Computational Testing
..................... 345
6.5.1
Some implementation details
.............. 345
6.5.2
Numerical results
.................... 351
6.5.3
Discussion
........................ 358
Bibliography
361
Index
391
|
| any_adam_object | 1 |
| author | Luo, Zhi-Quan Pang, Jong-Shi Ralph, Daniel |
| author_facet | Luo, Zhi-Quan Pang, Jong-Shi Ralph, Daniel |
| author_role | aut aut aut |
| author_sort | Luo, Zhi-Quan |
| author_variant | z q l zql j s p jsp d r dr |
| building | Verbundindex |
| bvnumber | BV035298318 |
| classification_rvk | SK 870 |
| classification_tum | MAT 910f |
| ctrlnum | (OCoLC)214307016 (DE-599)BVBBV035298318 |
| dewey-full | 519.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.7 |
| dewey-search | 519.7 |
| dewey-sort | 3519.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | digitally print. vers. |
| format | Book |
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| id | DE-604.BV035298318 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:30:43Z |
| institution | BVB |
| isbn | 9780521065085 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017103235 |
| oclc_num | 214307016 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-11 |
| owner_facet | DE-355 DE-BY-UBR DE-11 |
| physical | XXIV, 401 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Luo, Zhi-Quan Verfasser aut Mathematical programs with equilibrium constraints Zhi-Quan Luo ; Jong-Shi Pang ; Daniel Ralph digitally print. vers. Cambridge [u.a.] Cambridge Univ. Press 2008 XXIV, 401 S. txt rdacontent n rdamedia nc rdacarrier Programming (Mathematics) Nichtlineare Optimierung (DE-588)4128192-5 gnd rswk-swf Nichtlineare Optimierung (DE-588)4128192-5 s DE-604 Pang, Jong-Shi Verfasser aut Ralph, Daniel Verfasser aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017103235&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Luo, Zhi-Quan Pang, Jong-Shi Ralph, Daniel Mathematical programs with equilibrium constraints Programming (Mathematics) Nichtlineare Optimierung (DE-588)4128192-5 gnd |
| subject_GND | (DE-588)4128192-5 |
| title | Mathematical programs with equilibrium constraints |
| title_auth | Mathematical programs with equilibrium constraints |
| title_exact_search | Mathematical programs with equilibrium constraints |
| title_full | Mathematical programs with equilibrium constraints Zhi-Quan Luo ; Jong-Shi Pang ; Daniel Ralph |
| title_fullStr | Mathematical programs with equilibrium constraints Zhi-Quan Luo ; Jong-Shi Pang ; Daniel Ralph |
| title_full_unstemmed | Mathematical programs with equilibrium constraints Zhi-Quan Luo ; Jong-Shi Pang ; Daniel Ralph |
| title_short | Mathematical programs with equilibrium constraints |
| title_sort | mathematical programs with equilibrium constraints |
| topic | Programming (Mathematics) Nichtlineare Optimierung (DE-588)4128192-5 gnd |
| topic_facet | Programming (Mathematics) Nichtlineare Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017103235&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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