 Positively homogeneous function

ID: positively-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 + t Y) \geq f (X) + t f (Y),

because homogeneity rewrites the left-hand side as

(1 + t) f ((X + t Y) / (1 + t))

before concavity is applied.

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