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Smoothing a polyhedral convex function via cumulant transformation and homogenization

Alberto Seeger (1997)

Annales Polonici Mathematici

Given a polyhedral convex function g: ℝⁿ → ℝ ∪ +∞, it is always possible to construct a family g t > 0 which converges pointwise to g and such that each gₜ: ℝⁿ → ℝ is convex and infinitely often differentiable. The construction of such a family g t > 0 involves the concept of cumulant transformation and a standard homogenization procedure.

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