1. Not finding help here? Sign up for a free 30min 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!

Convex Function on Many variables on an interval

  1. Nov 3, 2012 #1
    1. The problem statement, all variables and given/known data
    Show that f(x) = x1x2 is a convex function on [a,ma]T where a [itex]\geq[/itex] 0
    and m [itex]\geq[/itex] 1.


    2. Relevant equations
    By definition f is convex iff

    [itex]\forall x,y\in \Re \quad \wedge \quad \forall \lambda :\quad 0\le \lambda \le 1\quad \Rightarrow \quad f\left( \lambda x+(1-\lambda )y \right) \le \lambda f\left( x \right) +(1-\lambda )f\left( y \right)[/itex]


    3. The attempt at a solution

    I am not really sure how to go about this. Firstly I was thinking on how to apply the above relation to multiple variables. I would assume that it applies in general and in this case x and y would be a vector of variables, but I still don't know how the proof follows. Also I am not sure is how the interval [a,ma]T plays into the equation.
     
    Last edited: Nov 3, 2012
  2. jcsd
  3. Nov 3, 2012 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    What is meant by [a,ma]T? I doubt that [a,ma] is a 1-dimensional interval, because what in the world would possibly be meant by the transpose of an interval? My guess would be that [a,ma] means a point in R2 of the form x1 = a, x2 = ma. However, that is just a guess.

    RGV
     
  4. Nov 3, 2012 #3
    Yes you are right in this, sorry I did not stipulate this, x1= a and x2=ma=mx1
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Convex Function on Many variables on an interval
  1. Convex function (Replies: 2)

  2. Convex functions (Replies: 2)

  3. Convex function (Replies: 4)

Loading...