Show Proving Convexity of f(x)=||x|| Function

[ahamdiheme]

How do i go about showing that if f(x)=$$\left\|$$x$$\left\|$$ then f(x) is a convex function.


I'm thinking in the direction of the triangle inequality but don't know how to go about it. Any clues? thanks

 

[tim_lou]

it just comes straight from definition of convex function

$$|tx+(1-t)y|\leq |tx| + |(1-t)y|$$

 

[ahamdiheme]

that is it, Thanks a lot!