Journal of Convex Analysis, Vol. 5, No. 2, pp. 397-403 (1998)

Homogeneous Functions and Conjugacy

Jean B. Lasserre

LAAS-CNRS, 7 Av. du Colonel Roche, 31077 Toulouse Cedex, France,

Abstract: (Positively) homogeneous functions play a special role in the Legendre-Fenchel duality. The Legendre-Fenchel conjugate of a $p$-homogeneous function is a $q$-homogeneous function with $1/p+1/q=1$. Further properties of the function, its conjugate, and of the maximizers are also derived. The same result also holds in the Max-Prod and Min-Max algebra for the analogue of the Legendre-Fenchel transform.

Keywords: Legendre-Fenchel duality, homogeneous functions

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