convex analysis

0.0.1 Convex sets

1. convex set

2. polyconvex set

3. extreme point

4. convex combination

5. Carathéodory’s theorem (http://planetmath.org/CaratheodorysTheorem2)

6. Radon’s lemma

7. Helly’s theorem

0.0.2 Topological properties of convex sets

1. Krein-Milman theorem

0.0.3 Convex functions

1. convex function

2. extremal value of convex/concave functions

3. logarithmically convex function

4. Jensen’s inequality

5. subdifferentiable mapping

0.0.4 Miscellaneous

1. Fenchel’s duality theorem

2. saddle function

3. minimax theory