Convex Analysis (Rockafellar, 1970)

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• Lean source path

Section index:

Chapter 01 -- Part I: Basic Concepts

• 1.1 Affine Sets

• 1.2 Convex Sets and Cones

• 1.3 The Algebra of Convex Sets

• 1.4 Convex Functions

• 1.5 Functional Operations

Chapter 02 -- Part II: Topological Properties

• 2.5 Functional Operations

• 2.6 Relative Interiors of Convex Sets

• 2.7 Closures of Convex Functions

• 2.8 Recession Cones and Unboundedness

• 2.9 Some Closedness Criteria

• 2.10 Continuity of Convex Functions

Chapter 03 -- Part III: Duality Correspondences

• 3.11 Separation Theorems

• 3.12 Conjugates of Convex Functions

• 3.13 Support Functions

• 3.14 Polars of Convex Sets

• 3.15 Polars of Convex Functions

• 3.16 Dual Operations

Chapter 04 -- Part IV: Representation and Inequalities

• 4.17 Caratheodory's Theorem

• 4.18 Extreme Points and Faces of Convex Sets

• 4.19 Polyhedral Convex Sets and Functions

• 4.20 Some Applications of Polyhedral Convexity