Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Help with Convex.

  1. Dec 3, 2008 #1
    How do i prove this?

    Let S = {(X1, …., Xn) € R^n | Xi ≥0, X1 + … +Xn = 1}. Show that S is convex.

    Suppose f(Si) = {X1, X2,..., Xn}
    AND g(Si) = {X1 + X2+ ....+Xn}

    but If do that, then f(Si) and g(Si), both will increase. Now I'm not sure where to go from here.

    *PS: Both functions are continuous convex function of Xi (Where = 1, 2, ..., N)

    Now as i mentioned earlier, both function increases, so does that also mean that S is convex?
    Last edited: Dec 3, 2008
  2. jcsd
  3. Dec 3, 2008 #2


    User Avatar
    Homework Helper

    Your notation is confusing. What is Si, and what is the target of the function f? What are you trying to do?

    Anyway, the way I'd do it is just to go back to the definition of a convex set. If X=(X1,...,Xn) and Y=(Y1,...,Yn) are in S, then show sX+(1-s)Y is in S for any s in [0,1]. This direct approach is easy enough in this situation.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?