Convexity of a function I don't understand

newphysist

Hi,

I am starting to learn real math I would say for first time in life. I have come across this function:

Code:

f(x) = max_i(x_i) - min_i(x_i)

The domain is R.

Does the above function mean f(x) = 0 since for for x in R max and min of x would be x itself.

Hence it is convex as for any θ ≥ 0 we can write:

Code:

θ.x + (1-θ).y = 0 ≤ f(θ.x + (1-θ).y)
f(θ.x + (1-θ).y) = 0

In above both x and y would be any R.

Thanks for helping me learn.

Yuu Suzumi

Is the argument of [itex] f [/itex] perhaps a vector and the [itex] x_i [/itex] the components thereof? I am sure they are not meant to be the same.

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Yuu Suzumi Recognitions: Gold Member	Is the argument of [itex] f [/itex] perhaps a vector and the [itex] x_i [/itex] the components thereof? I am sure they are not meant to be the same.