Muutke küpsiste eelistusi

Mathematical Programs with Equilibrium Constraints [Pehme köide]

(McMaster University, Ontario), (University of Melbourne), (The Johns Hopkins University)
  • Formaat: Paperback / softback, 428 pages, kõrgus x laius x paksus: 229x151x24 mm, kaal: 622 g, 4 Tables, unspecified
  • Ilmumisaeg: 12-Jun-2008
  • Kirjastus: Cambridge University Press
  • ISBN-10: 0521065089
  • ISBN-13: 9780521065085
Teised raamatud teemal:
Mathematical Programs with Equilibrium ConstraintsSuurem pilt
  • Formaat: Paperback / softback, 428 pages, kõrgus x laius x paksus: 229x151x24 mm, kaal: 622 g, 4 Tables, unspecified
  • Ilmumisaeg: 12-Jun-2008
  • Kirjastus: Cambridge University Press
  • ISBN-10: 0521065089
  • ISBN-13: 9780521065085
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780521065085.html
Märksõnad:
An extensive study for an important class of constrained optimisation problems known as Mathematical Programs with Equilibrium Constraints.

This book provides a solid foundation and an extensive study for Mathematical Programs with Equilibrium Constraints (MPEC). It begins with the description of many source problems arising from engineering and economics that are amenable to treatment by the MPEC methodology. Error bounds and parametric analysis are the main tools to establish a theory of exact penalization, a set of MPEC constraint qualifications and the first-order and second-order optimality conditions. The book also describes several iterative algorithms such as a penalty based interior point algorithm, an implicit programming algorithm and a piecewise sequential quadratic programming algorithm for MPECs. Results in the book are expected to have significant impacts in such disciplines as engineering design, economics and game equilibria, and transportation planning, within all of which MPEC has a central role to play in the modeling of many practical problems.

Arvustused

"The book provides a good basis for further theoretical and applications-oriented investigations of MPECs. This monograph can be recommended as a valuable resource in applied mathematics, especially in the fields of operations research and engineering, as well as for specialists in mathematical prgramming." Stephen Dempe,Mathematical Reviews

Muu info

An extensive study for an important class of constrained optimisation problems known as Mathematical Programs with Equilibrium Constraints.
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
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. multipliers
213
4.4 An Exact Penalty Equivalent of Order
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
249
5.5 KKT Constrained Mathematical Program
254
5.3 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
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