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| 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. |
| 1 Introduction 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 3 Variational 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 4 Variational 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 5 Variational 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 |
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