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Convex Function

  1. Nov 19, 2008 #1
    1. The problem statement, all variables and given/known data

    Let f:Rn[tex]\rightarrow[/tex]Rnxmtex] and b[tex]\in[/tex]Rn. Define g:Rm[tex]\rightarrow[/tex]R by
    g=f(Ax+b)
    Show that g is convex if f is convex

    2. Relevant equations



    3. The attempt at a solution
    I need hints on how to go about this please.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 19, 2008 #2
    Hi ahamdiheme,

    What is the definition of a convex function? Immediately from that you should realise that f must be real-valued in order to be convex; also, I assume A is an nxm matrix.

    To get the manipulation right in the inequality (when you look to apply the definition), it will help to write down what you want to arrive at to make the manipulation easier.

    Show your work if you get stuck.
     
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