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Bi-Level Strategies in Semi-Infinite Programming 2003 ed. [Kõva köide]

  • Formaat: Hardback, 202 pages, kõrgus x laius: 235x155 mm, kaal: 1120 g, XXVIII, 202 p., 1 Hardback
  • Sari: Nonconvex Optimization and Its Applications 71
  • Ilmumisaeg: 31-Aug-2003
  • Kirjastus: Springer-Verlag New York Inc.
  • ISBN-10: 1402075677
  • ISBN-13: 9781402075674
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Bi-Level Strategies in Semi-Infinite Programming 2003 ed.Suurem pilt
  • Formaat: Hardback, 202 pages, kõrgus x laius: 235x155 mm, kaal: 1120 g, XXVIII, 202 p., 1 Hardback
  • Sari: Nonconvex Optimization and Its Applications 71
  • Ilmumisaeg: 31-Aug-2003
  • Kirjastus: Springer-Verlag New York Inc.
  • ISBN-10: 1402075677
  • ISBN-13: 9781402075674
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781402075674.html
Märksõnad:
In this text for advanced students and researchers in optimization and operations research, Stein (mathematics, Aachen University, Germany), explores the bi-level structure of semi-infinite programming, highlights topological and structural aspects of general semi-infinite programming, formulates optimality conditions which take this structure into account, and offers a new bi-level solution method. Results are illustrated by problems from engineering and economics that give rise to semi-infinite models, including minimax problems, robust optimization, design centering, and disjunctive programming. Annotation (c) Book News, Inc., Portland, OR (booknews.com)

This is the first book that exploits the bi-level structure of semi-infinite programming systematically. It highlights topological and structural aspects of general semi-infinite programming, formulates powerful optimality conditions, which take this structure into account, and gives a conceptually new bi-level solution method. The results are motivated and illustrated by a number of problems from engineering and economics that give rise to semi-infinite models, including (reverse) Chebyshev approximation, minimax problems, robust optimization, design centering, defect minimization problems for operator equations, and disjunctive programming. Audience: The book is suitable for graduate students and researchers in the fields of optimization and operations research.

Arvustused

From the reviews:



"This is the first book which exploits the bilevel structure of semi-infinite programming systematically. It highlights topological and structural aspects of general semi-infinite programming, formulates powerful optimality conditions, and gives a conceptually new bilevel solution method. The book is addressed to graduate students and researchers who work in the fields of optimization and operations research." (Oliver Stein, Zentralblatt MATH, Vol. 1103 (5), 2007)

List of Symbols xi
List of Figures xv
List of Tables xix
Preface xxi
Acknowledgments xxvii
1. INTRODUCTION 1(10)
1.1 Standard semi-infinite programming
2(2)
1.2 General semi-infinite programming
4(2)
1.3 The misconception about the generality of GSIP
6(2)
1.4 Development to a field of active research
8(3)
2. EXAMPLES AND APPLICATIONS 11(14)
2.1 Chebyshev and reverse Chebyshev approximation
12(2)
2.2 Minimax problems
14(1)
2.3 Robust optimization
15(3)
2.4 Design centering
18(2)
2.5 Defect minimization for operator equations
20(2)
2.6 Disjunctive programming
22(3)
3. TOPOLOGICAL STRUCTURE OF THE FEASIBLE SET 25(60)
3.1 Abstract index set mappings
25(21)
3.1.1 A projection formula
21(10)
3.1.2 A bi-level formula and semi-continuity properties
31(10)
3.1.3 A set-valued mapping formula
41(1)
3.1.4 The local structure of M
42(2)
3.1.5 The completely convex case
44(2)
3.2 Index set mappings with functional constraints
46(39)
3.2.1 The convex case
46(1)
3.2.2 The linear case
47(13)
3.2.3 The C1 case
60(2)
3.2.4 The C2 case
62(4)
3.2.5 Genericity results
66(19)
4. OPTIMALITY CONDITIONS 85(60)
4.1 Abstract primal optimality conditions
85(5)
4.2 First order approximations of the feasible set
90(26)
4.2.1 General constraint qualifications
91(5)
4.2.2 Descriptions of the linearization cones
96(12)
4.2.3 Degenerate index sets
108(8)
4.3 Dual first order optimality conditions
116(26)
4.3.1 The standard semi-infinite case
118(2)
4.3.2 The completely convex case
120(3)
4.3.3 The convex case
123(3)
4.3.4 The C2 case with Reduction Ansatz
126(2)
4.3.5 The C1 case
128(14)
4.4 Second order optimality conditions
142(3)
5. BI-LEVEL METHODS FOR GSIP 145(26)
5.1 Reformulations of GSIP
146(8)
5.1.1 The Stackelberg game reformulation of GSIP
146(2)
5.1.2 The MPEC reformulation of GSIP
148(1)
5.1.3 A regularization of MPEC by NCP functions
149(3)
5.1.4 The regularized Stackelberg game
152(2)
5.2 Convergence results for a bi-level method
154(13)
5.2.1 A parametric reduction lemma
155(2)
5.2.2 Convergence of global solutions
157(1)
5.2.3 Convergence of Fritz John points
158(4)
5.2.4 Quadratic convergence of the optimal values
162(1)
5.2.5 An outer approximation property
163(4)
5.3 Other bi-level approaches and generalizations
167(4)
6. COMPUTATIONAL RESULTS 171(16)
6.1 Design centering in two dimensions
172(5)
6.2 Design centering in higher dimensions
177(1)
6.3 Robust optimization
178(3)
6.4 Optimal error bounds for an elliptic operator equation
181(6)
7. FINAL REMARKS 187(4)
References 191(10)
Index 201