Mathematical programs with equilibrium constraints:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
1996
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XXIV, 401 S. |
| ISBN: | 0521572908 9780521572903 9780521065085 |
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| 245 | 1 | 0 | |a Mathematical programs with equilibrium constraints |c Zhi-Quan Luo ; Jong-Shi Pang ; Daniel Ralph |
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| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 1996 | |
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Record in the Search Index
| _version_ | 1804125712998727680 |
|---|---|
| adam_text | MATHEMATICAL PROGRAMS WITH EQUILIBRIUM CONSTRAINTS ZHI-QUAN LUO MCMASTER
UNIVERSITY JONG-SHI PANG THE JOHNS HOPKINS UNIVERSITY DANIEL RALPH THE
UNIVERSITY OF MELBOURNE CAMBRIDGE UNIVERSITY PRESS 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 FULL 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 C. |
| author_facet | Luo, Zhi-Quan Pang, Jong-Shi Ralph, Daniel C. |
| author_role | aut aut aut |
| author_sort | Luo, Zhi-Quan |
| author_variant | z q l zql j s p jsp d c r dc dcr |
| building | Verbundindex |
| bvnumber | BV011214966 |
| classification_rvk | SK 870 |
| classification_tum | MAT 910f |
| ctrlnum | (OCoLC)243855675 (DE-599)BVBBV011214966 |
| dewey-full | 519.76 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.76 |
| dewey-search | 519.76 |
| dewey-sort | 3519.76 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:05:56Z |
| institution | BVB |
| isbn | 0521572908 9780521572903 9780521065085 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007523620 |
| oclc_num | 243855675 |
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| physical | XXIV, 401 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| 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 1. publ. Cambridge [u.a.] Cambridge Univ. Press 1996 XXIV, 401 S. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke 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 C. Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007523620&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Luo, Zhi-Quan Pang, Jong-Shi Ralph, Daniel C. Mathematical programs with equilibrium constraints 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 | Nichtlineare Optimierung (DE-588)4128192-5 gnd |
| topic_facet | Nichtlineare Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007523620&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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