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