For every sublinear function and convex cone, the paper characterizes all optimally smooth approximations as the interval between two explicit extremal smoothings.
On a class of nonsmooth composite functions.Mathematics of Operations Research, 28(4):677–692, 2003
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The Optimal Smoothings of Sublinear Functions and Convex Cones
For every sublinear function and convex cone, the paper characterizes all optimally smooth approximations as the interval between two explicit extremal smoothings.