Convex Analysis

This group gathers theorems about convex sets, convex functions, and the inequalities and extremal principles built from them, a strand of analysis that runs through optimization, functional analysis, and geometry alike. It covers extreme-point results such as the Krein-Milman theorem, classical inequalities including the arithmetic-geometric mean and Minkowski's inequality, and optimization-flavored results, including Danskin's theorem and the Bauer maximum principle, that describe how convexity forces the extreme values of a function to be attained.