Mathematical Methods for Optimization
Carathéodory's Theorem states that if a point in a convex set can be expressed as a convex combination of other points from that set, then it can be represented as a convex combination of at most 'd+1' points, where 'd' is the dimension of the convex set. This theorem provides a way to simplify complex problems involving convex combinations and is fundamental in understanding the properties of convex sets and functions.
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