Smoothing a polyhedral convex function via cumulant transformation and homogenization
Volume 67 / 1997
Annales Polonici Mathematici 67 (1997), 259-268
DOI: 10.4064/ap-67-3-259-268
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.
