Convex function

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Let LaTeX: f:X\rightarrow R. Then LaTeX: f is convex if 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) \le af(x) + (1-a)f(y).

Equivalently, its epigraph is convex.


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