Is $f(x,y) = x - y$ convex?

Question

I know that linear functions are both convex and concave, except the negative summation does not uphold the convexity. Due to this fact, is it safe to assume that $f(x,y) = x-y$ is not convex?

$x-y$ is linear and so it's convex. – CyclotomicField Jan 19 '20 at 19:37 — CyclotomicField, Jan 19 '20 at 19:37

score 0 · Accepted Answer · answered Jan 19 '20 at 19:51

0

Every real-valued linear transformation is convex but not strictly convex, since if $f$ is linear, then $f(a+b)=f(a)+f(b)$.

answered Jan 19 '20 at 19:51

idriskameni

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Is $f(x,y) = x - y$ convex?

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