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A function that is never below its linear interpolation. Mathematically, a function f (x) is concave over a convex set S, if for any two points, x1 and x2 in S and for any 0 ≤ α ≤ 1, f [αx1 + (1 − α)x2] ≥ α f (x1) + (1 − α) f (x2).
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