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Abstract

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