Positively homogeneous function (source code)

= Positively homogeneous function
{wiki=Homogeneous_function}

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.

= Positive homogeneity
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= Positively homogeneous
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