Régularisation d'ordre supérieur d'une fonction convexe polyhédrale : considérations géométriques et probabilistes
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This Note deals with a higher order smoothing technique for a polyhedral convex function f:Rn→R
{+∞}. This technique consists in approximating f by a family {ft}t>0, with ft:Rn→R being convex and infinitely often differentiable. The explicit formula for ft is given in terms of a function M:Rn×R→R whose expression is derived straightforwardly from the canonical representation of f. We show that M generates a wealth of information on the behaviour of f.
{+∞}. This technique consists in approximating f by a family {ft}t>0, with ft:Rn→R being convex and infinitely often differentiable. The explicit formula for ft is given in terms of a function M:Rn×R→R whose expression is derived straightforwardly from the canonical representation of f. We show that M generates a wealth of information on the behaviour of f.