# Smoothing a polyhedral convex function via cumulant transformation and homogenization

Annales Polonici Mathematici (1997)

- Volume: 67, Issue: 3, page 259-268
- ISSN: 0066-2216

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topAlberto Seeger. "Smoothing a polyhedral convex function via cumulant transformation and homogenization." Annales Polonici Mathematici 67.3 (1997): 259-268. <http://eudml.org/doc/270164>.

@article{AlbertoSeeger1997,

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.},

author = {Alberto Seeger},

journal = {Annales Polonici Mathematici},

keywords = {polyhedral convex function; smooth approximation; Laplace transformation; cumulant transformation; homogenization; recession function},

language = {eng},

number = {3},

pages = {259-268},

title = {Smoothing a polyhedral convex function via cumulant transformation and homogenization},

url = {http://eudml.org/doc/270164},

volume = {67},

year = {1997},

}

TY - JOUR

AU - Alberto Seeger

TI - Smoothing a polyhedral convex function via cumulant transformation and homogenization

JO - Annales Polonici Mathematici

PY - 1997

VL - 67

IS - 3

SP - 259

EP - 268

AB - 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.

LA - eng

KW - polyhedral convex function; smooth approximation; Laplace transformation; cumulant transformation; homogenization; recession function

UR - http://eudml.org/doc/270164

ER -

## References

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- [12] A. Seeger, Smoothing a nondifferentiable convex function: the technique of the rolling ball, Technical Report 165, Dep. of Mathematical Sciences, King Fahd Univ. of Petroleum and Minerals, Dhahran, Saudi Arabia, October 1994. Zbl0921.49008
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