Positively homogeneous function (degree one)
= Positively homogeneous function
{disambiguate=degree one}
= Positively homogeneous function
{synonym}
= Positive homogeneity
{synonym}
= Positively homogeneous
{synonym}
A <function> on a cone is positively homogeneous of degree one when $f(tX)=t f(X)$ for every $t>0$. If such a function is <concave>, then
$$
f(X+tY)\geq f(X)+t f(Y),
$$
because homogeneity rewrites the left-hand side as $(1+t)f((X+tY)/(1+t))$ before <concavity> is applied.