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Convexity of a function I don't understand

  1. Nov 14, 2012 #1
    Hi,

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

    Code (Text):

    f(x) = max[SUB]i[/SUB](x[SUB]i[/SUB]) - min[SUB]i[/SUB](x[SUB]i[/SUB])
     
    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 (Text):

    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.
     
  2. jcsd
  3. Nov 14, 2012 #2
    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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