I Topics in Real Analysis 1
1. Introduction 1
2. Vectors in R 1
3. Algebra of Sets 4
4. Metric Topology of R 5
5. Limits and Continuity 8
6. Basic Property of Real Numbers 11
7. Compactness 14
8. Equivalent Norms and Cartesian Products 16
9. Fundamental Existence Theorem 18
10. Linear Transformations 21
11. Differentiation in R 22
II Convex Sets in Rn 30
1. Lines and Hyperplanes in R 30
2. Properties of Convex Sets 35
3. Separation Theorems 45
4. Supporting Hyperplanes: Extreme Points 56
5. Systems of Linear Inequalities: Theorems of the Alternative 61
6. Affine Geometry 69
7. More on Separation and Support 80
III Convex Functions 87
1. Definition and Elementary Properties 87
2. Subgradients 102
3. Differentiable Convex Functions 106
4. Alternative Theorems for Convex Functions 113
5. Application to Game Theory 117
vIV Optimization Problem
V Convex Programming and Duality 179
1. Problem Statement 179
2. Necessary Conditions and Sufficient Conditions 181
3. Perturbation Theory 188
4. Lagrangian Duality 200
5. Geometric Interpretation 207
6. Quadratic Programming 210
7. Duality in Linear Programming 215
VI Simplex Method 222
1. Introduction 222
2. Extreme Points of Feasible Set 225
3. Preliminaries to Simplex Method 230
4. Phase II of Simplex Method 234
5. Termination and Cycling 245
6. Phase I of Simplex Method 251
7. Revised Simplex Method
由于内容很多...所以指摘了几张的目录共参考..............
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