1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Convexity of a function I don't understand

  1. Nov 14, 2012 #1

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook