Geodesic
Smoothing a polyhedral convex function via cumulant transformation and homogenization
Annales Polonici Mathematici, Tome 67 (1997) no. 3, pp. 259-268
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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.
DOI : 10.4064/ap-67-3-259-268
Keywords: polyhedral convex function, smooth approximation, Laplace transformation, cumulant transformation, homogenization, recession function 
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     title = {Smoothing a polyhedral convex function via cumulant transformation and homogenization},
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Alberto Seeger. Smoothing a polyhedral convex function via cumulant transformation and homogenization. Annales Polonici Mathematici, Tome 67 (1997) no. 3, pp. 259-268. doi: 10.4064/ap-67-3-259-268

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