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Regularity Concepts in Nonsmooth Analysis: Theory and Applications 2012 [Kõva köide]

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  • Formaat: Hardback, 264 pages, kõrgus x laius: 235x155 mm, kaal: 588 g, XVI, 264 p., 1 Hardback
  • Sari: Springer Optimization and Its Applications 59
  • Ilmumisaeg: 12-Nov-2011
  • Kirjastus: Springer-Verlag New York Inc.
  • ISBN-10: 1461410185
  • ISBN-13: 9781461410188
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Regularity Concepts in Nonsmooth Analysis: Theory and Applications 2012Suurem pilt
  • Formaat: Hardback, 264 pages, kõrgus x laius: 235x155 mm, kaal: 588 g, XVI, 264 p., 1 Hardback
  • Sari: Springer Optimization and Its Applications 59
  • Ilmumisaeg: 12-Nov-2011
  • Kirjastus: Springer-Verlag New York Inc.
  • ISBN-10: 1461410185
  • ISBN-13: 9781461410188
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781461410188.html
Märksõnad:

The results presented in this book are a product of research conducted by the author independently and in collaboration with other researchers in the field. In this light, this work encompasses the most recent collection of various concepts of regularity and nonsmooth analysis into one monograph. The first part of the book attempts to present an accessible and thorough introduction to nonsmooth analysis theory. Main concepts and some useful results are stated and illustrated through examples and exercises. The second part gathers the most prominent and recent results of various regularity concepts of sets, functions, and set-valued mappings in nonsmooth analysis. The third and final section contains six different application, with comments in relation to the existing literature.

Part I Nonsmooth Analysis Theory
1 Nonsmooth Concepts
3(30)
1.1 Introduction
3(1)
1.2 From Derivatives to Subdifferentials
4(6)
1.2.1 Unconstrained Minimization Problems
5(3)
1.2.2 Constrained Minimization Problems
8(2)
1.3 Subdifferentials
10(7)
1.3.1 The Generalized Gradient (Clarke Subdifferential)
10(5)
1.3.2 Other Concepts of Subdifferentials
15(2)
1.4 Tangent Cones
17(2)
1.5 Normal Cones
19(10)
1.5.1 The Convexified (Clarke) Normal Cone
20(1)
1.5.2 The Proximal Normal Cone
20(5)
1.5.3 The Frechet Normal Cone (Prenormal cone)
25(2)
1.5.4 The Basic Normal Cone (Limiting Normal Cone or Mordukhovich Normal Cone)
27(2)
1.6 Commentary to Chap. 1
29(4)
Part II Regularity Concepts in Nonsmooth Analysis Theory
2 Regularity of Sets
33(40)
2.1 Motivations
33(2)
2.1.1 Calculus Rules
33(1)
2.1.2 Differential Inclusions
34(1)
2.2 Tangential Regularity of Sets
35(2)
2.3 Frechet and Proximal Normal Regularity of Sets
37(1)
2.4 Scalar Regularity of Sets
37(3)
2.5 Scalarization of Tangential Regularity: [ (TR) ⇔ (DR)?]
40(4)
2.6 Scalarization of Frechet Normal Regularity: [ (FNR) ⇔ (FSR)]?
44(3)
2.7 Scalarization of Proximal Normal Regularity: [ (PNR) ⇔ (PSR)]?
47(2)
2.8 Weak Tangential Regularity of Sets
49(6)
2.9 Uniform Prox-Regularity of Sets
55(5)
2.10 Arc-Wise Essential Tangential Regularity
60(4)
2.11 More on the Regularity of Sets
64(7)
2.11.1 Frechet Case
64(4)
2.11.2 Proximal Case
68(3)
2.12 Commentary to Chap. 2
71(2)
3 Regularity of Functions
73(14)
3.1 Introduction
73(4)
3.2 Directional Regularity of Functions
77(6)
3.3 Frechet and Proximal Subdifferential Regularity of Functions
83(2)
3.4 Commentary to Chap. 3
85(2)
4 Regularity of Set-Valued Mappings
87(40)
4.1 Introduction
87(1)
4.2 On the Distance Function to Images ΔM Around Points on the Graph
88(6)
4.3 Tangential Regularity of gph M and Directional Regularity of ΔM
94(9)
4.4 Tangential Regularity of Lipschitz Epigraphic Set-Valued Mappings
103(9)
4.5 Tangential Regularity of Images
112(1)
4.6 On the Distance Function to Images Around Points Outside the Graph
113(7)
4.7 Application of ΔM: Calmness and Exact Penalization
120(4)
4.8 Commentary to Chap. 4
124(3)
Part III Applications of Nonsmooth Analysis Theory
5 First Order Differential Inclusions
127(38)
5.1 Nonconvex Sweeping Processes and Nonconvex Differential Inclusions
127(11)
5.1.1 Introduction
127(1)
5.1.2 Equivalence Between Nonconvex Sweeping Process and a Particular Nonconvex Differential Inclusion
128(7)
5.1.3 Existence Results: Finite Dimensional Case
135(3)
5.2 Existence of Viable Solutions of Nonconvex First Order Differential Inclusions
138(9)
5.2.1 Introduction
138(1)
5.2.2 Existence Criteria of Viable Solutions of Nonconvex Differential Inclusions
138(9)
5.3 Existence Results for First Order Nonconvex Sweeping Processes: Infinite Dimensional Case
147(8)
5.4 First Order Perturbed Nonconvex Sweeping Process with Delay
155(9)
5.4.1 Introduction
155(9)
5.5 Commentary to Chap. 5
164(1)
6 Second Order Differential Inclusions
165(46)
6.1 Introduction
165(2)
6.2 Existence Theorems: Fixed Point Approach
167(9)
6.3 Existence Theorems: Direct Approach
176(21)
6.4 Properties of Solution Sets
197(2)
6.5 Particular Case
199(2)
6.6 Second Order Perturbed Sweeping Process with Delay
201(8)
6.6.1 Existence Theorems
201(8)
6.7 Commentary to Chap. 6
209(2)
7 Quasi-Variational Inequalities
211(16)
7.1 Introduction
211(3)
7.2 Main Theorems
214(5)
7.3 Extensions
219(6)
7.4 Commentary to Chap. 7
225(2)
8 Economic Problems and Equilibrium Theory
227(20)
8.1 Introduction
227(1)
8.2 Uniform Prox-Regularity of Level Sets and Uniform Lower-C2 Property
228(8)
8.3 Subdifferential and Co-normal Stability
236(3)
8.4 Nonconvex Nontransitive Economies
239(4)
8.5 Existence of Nonconvex Equilibrium
243(3)
8.6 Commentary to Chap. 8
246(1)
References 247(12)
Index 259