Monotonic function

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A function that either never decreases or never increases. A non-decreasing, or isotonic, function satisfies: LaTeX: f(x') \ge f(x) whenever LaTeX: x' \ge x (it is strictly increasing if LaTeX: f(x') > f(x) for LaTeX: x' > x). A non-increasing, or anatonic, function satisfies: LaTeX: f(x') \le f(x) whenever LaTeX: x' \ge x (it is strictly decreasing if LaTeX: f(x') < f(x) for LaTeX: x'> x). This extends to a vector function, where LaTeX: \mbox{range}(f) is in LaTeX: \mathbb{R}^n: LaTeX: (f(x)-f(x))^T (x-y) \ge 0.


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