let $x=x_1,x_2,…,x_n$ for $x \ge 0$,
let $I(x) =max(x_i, 0) $ for $i \in [1,n]$
$f(x) = I(c-x)a^T+I(x-c)b^T$ where $a,b,c$ are constant vectors
Is this a convex function? How is this proven?
convex optimizationconvex-analysisnon-convex-optimizationnonlinear optimizationoptimization
let $x=x_1,x_2,…,x_n$ for $x \ge 0$,
let $I(x) =max(x_i, 0) $ for $i \in [1,n]$
$f(x) = I(c-x)a^T+I(x-c)b^T$ where $a,b,c$ are constant vectors
Is this a convex function? How is this proven?
Best Answer
Yes, $f$ is a convex function. You just need to know some some basic properties that imply convexity:
From that we have: