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Convex analysis

Dodecahedron

There are two kinds of convex analysis that I know a bit, corresponding to rather distinct scientific communities, taking their roots in the works of Minkowski, Carathéodory, Krein, Fenchel, Tucker, Milman I, and many others. Both domains concern finite dimensional spaces. The first one is more concerned with optimization algorithms in fixed dimension (possibly large nowadays), while the second is related to Banach spaces and involves asymptotic geometric analysis in which the dimension is often high. Both domains are connected to geometry, to probability theory, and to statistics. Here are some of the classical books (not all of them!):

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