Convex Function Calculus
- If and are convex functions, then so are and
- If and are convex functions and is non-decreasing, then is convex. As an example, if is convex, then so is, because is convex and monotonically increasing.
- If is concave and is convex and non-increasing, then is convex.
- Convexity is invariant under affine maps: that is, if is convex with, then so is, where
- If is convex in then is convex in provided for some
- If is convex, then its perspective (whose domain is ) is convex.
- The additive inverse of a convex function is a concave function.
Read more about this topic: Convex Function
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