Techniques of variational analysis变异分析的技术
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作者： Jonathan M. Borwein，Qiji J. Zhu著
出 版 社：
出版时间： 2005-6-1字数：版次： 1页数： 362印刷时间： 2005/06/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780387242989包装： 精装编辑推荐
作者简介：Jonathan M. Borwein, FRSC is Canada Research Chair in Collaborative Technology at Dalhousie University. He received his Doctorate from Oxford in 1974 and has been on faculty at Waterloo, Carnegie Mellon and Simon Fraser Universities. He has published extensively in optimization, analysis and computational mathematics and has received various prizes both for research and for exposition.
内容简介
Variational arguments are classical techniques whose use can be traced back to the early development of the calculus of variations and further. Rooted in the physical principle of least action, they have wide applications in diverse fields. This book provides a concise account of the essential tools of infinite-dimensional first-order variational analysis. These tools are illustrated by applications in many different parts of analysis, optimization and approximation, dynamical systems, mathematical economics and elsewhere. Much of the material in the book grows out of talks and short lecture series given by the authors in the past several years. Thus, chapters in this book can easily be arranged to form material for a graduate level topics course. A sizeable collection of suitable exercises is provided for this purpose. In addition, this book is also a useful reference for researchers who use variational techniques - or just think they might like to.
目录
1Introduction
1.1 Introduction
1.2 Notation
1.3 Exercises
2 Variational Principles
2.1 Ekeland Variational Principles
2.2 Geometric Forms of the Variational Principle
2.3 Applications to Fixed Point Theorems
2.4 Finite Dimensional Variational Principles
2.5 Borwein Preiss Variational Principles
3Variational Techniques in Subdifferential Theory
3.1 The Frechet Subdifferential and Normal Cone
3.2 Nonlocal Sum Rule and Viscosity Solutions
3.3 Local Sum Rules and Constrained Minimization
3.4 Mean Value Theorems and Applications
3.5 Chain Rules and Lyapunov Functions
3.6 Multidireetional MVI and Solvability
3.7 Extremal Principles
4Variational Techniques in Convex Analysis
4.1 Convex Functions and Sets
4.2 Subdifferential
4.3 Sandwich Theorems and Calculus
4.4 Fenchel Conjugate
4.5 Convex Feasibility Problems
4.6 Duality Inequalities for Sandwiched Functions
4.7 Entropy Maximization
5Variational Techniques and Multifunctions
5.1 Multifunctions
5.2 Subdifferentials as Multifunctions
5.3 Distance Functions
5.4 Coderivatives of Multifunctions
5.5 Implicit Multifunction Theorems
Variational Principles in Nonlinear Functional Analysis
6.1 Subdifferential and Asplund Spaces
6.2 Nonconvex Separation Theorems
6.3 Stegall Variational Principles
6.4 Mountain Pass Theorem
6.5 One-Perturbation Variational Principles
Variational Techniques in the Presence of Symmetry
7.1 Nonsmooth Functions on Smooth Manifolds
7.2 Manifolds of Matrices and Spectral Functions
7.3 Convex Spectral Functions
References
Index
