Muutke küpsiste eelistusi

Bi-Level Strategies in Semi-Infinite Programming Softcover reprint of the original 1st ed. 2003 [Pehme köide]

  • Formaat: Paperback / softback, 202 pages, kõrgus x laius: 235x155 mm, kaal: 367 g, XXVIII, 202 p., 1 Paperback / softback
  • Sari: Nonconvex Optimization and Its Applications 71
  • Ilmumisaeg: 26-Nov-2013
  • Kirjastus: Springer-Verlag New York Inc.
  • ISBN-10: 146134817X
  • ISBN-13: 9781461348177
Teised raamatud teemal:
  • Pehme köide
  • Hind: 132,08 €*
  • * hind on lõplik, st. muud allahindlused enam ei rakendu
  • Tavahind: 155,39 €
  • Säästad 15%
  • Raamatu kohalejõudmiseks kirjastusest kulub orienteeruvalt 2-4 nädalat
  • Kogus:
  • Lisa ostukorvi
  • Tasuta tarne
  • Tellimisaeg 2-4 nädalat
  • Lisa soovinimekirja
Bi-Level Strategies in Semi-Infinite Programming Softcover reprint of the original 1st ed. 2003Suurem pilt
  • Formaat: Paperback / softback, 202 pages, kõrgus x laius: 235x155 mm, kaal: 367 g, XXVIII, 202 p., 1 Paperback / softback
  • Sari: Nonconvex Optimization and Its Applications 71
  • Ilmumisaeg: 26-Nov-2013
  • Kirjastus: Springer-Verlag New York Inc.
  • ISBN-10: 146134817X
  • ISBN-13: 9781461348177
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781461348177.html
Märksõnad:
Semi-infinite optimization is a vivid field of active research. Recently semi­ infinite optimization in a general form has attracted a lot of attention, not only because of its surprising structural aspects, but also due to the large number of applications which can be formulated as general semi-infinite programs. The aim of this book is to highlight structural aspects of general semi-infinite programming, to formulate optimality conditions which take this structure into account, and to give a conceptually new solution method. In fact, under certain assumptions general semi-infinite programs can be solved efficiently when their bi-Ievel structure is exploited appropriately. After a brief introduction with some historical background in Chapter 1 we be­ gin our presentation by a motivation for the appearance of standard and general semi-infinite optimization problems in applications. Chapter 2 lists a number of problems from engineering and economics which give rise to semi-infinite models, including (reverse) Chebyshev approximation, minimax problems, ro­ bust optimization, design centering, defect minimization problems for operator equations, and disjunctive programming.

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)

Muu info

Springer Book Archives
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
27(4)
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