| Introduction Part I. Nonlinear Analysis: Theory 1. Minimisation Problems: General Theorems 1.1 Introduction 1.2 Definitions 1.3 Epigraph 1.4 Lower Sections 1.5 Lower Semi-continuous Functions 1.6 Lower Semi-compact Functions 1.7 Approximate Minimisation of Lower Semi-continuous Functions on a Complete Space 1.8 Application to Fixed-point Theorems 2. Convex Functions and Proximation， Projection and Separation Theorems 2.1 Introduction 2.2 Definitions 2.3 Examples of Convex Functions 2.4 Continuous Convex Functions 2.5 The Proximation Theorem 2.6 Separation Theorems 2.6 Separation Theorems 3. Conjugate Functions and Convex Minimisation Problems 3.1 Introduction 3.2 Characterisation of Convex Lower Semi-continuous Functions 3.3 Fenchel's Theorem 3.4 Properties of Conjugate Functions 3.5 Support Functions 4. Subdifferentials of Convex Functions 4.1 Introduction 4.2 Definitions 4.3 Subdifferentiability of Convex Continuous Functions 4.4 Subdifferentiability of Convex Lower Semi-continuous Functions 4.5 Subdifferential Calculus 4.6 Tangent and Normal Cones 5. Marginal Properties of Solutions of Convex Minimisation Problems 5.1 Introduction 5.2 Fermat's Rule 5.3 Minimisation Problems with Constraints 5.4 Principle of Price Decentralisation 5.5 Regularisation and Penalisation 6. Generalised Gradients of Locally Lipschitz Functions 6.1 Introduction 6.2 Definitions 6.3 Elementary Properties 6.4 Generalised Gradients 6.5 Normal and Tangent Cones to a Subset 6.6 Fermat's Rule for Minimisation Problems with Constraints 7. Two-person Games. Fundamental Concepts and Examples 7.1 Introduction 7.2 Decision Rules and Consistent Pairs of Strategies 7.3 Brouwer's Fixed-point Theorem (1910) 7.4 The Need to Convexify: Mixed Strategies 7.5 Games in Normal (Strategic) Form 7.6 Pareto Optima 7.7 Conservative Strategies 7.8 Some Finite Games 7.9 Cournot's Duopoly 8. Two-person Zero-sum Games: Theorems of Von Neumannand Ky Fan 9. Solution of Nonlinear Equatioris and Inclusions 10. Introduction to the Theory of Economic Equilibrium 11. The Von Neumann Growth Model 12. n-person Games 13. Cooperative Games and Fuzzy Games Part Ⅱ. Nonlinear Analysis: Examples 15. Statements of Problems 16. Solutions to Problems Appendix 17. Compendium of Results References Subject Index |
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