Concave function

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The real valued function LaTeX: f is concave if its domain, say LaTeX: X, is a convex set, and for LaTeX: x, y \in X and LaTeX: 0 \le a \le 1:

LaTeX: 
f(ax + (1-a)y) \ge af(x) + (1-a)f(y).
Equivalently, LaTeX: f is concave if its hypograph is a convex set or if its negative is a convex function.


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