Benjamin Grimmer

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20242026

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math.ST2025

An Elementary Proof of the Near Optimality of LogSumExp Smoothing

Thabo Samakhoana, Benjamin Grimmer

We consider the design of smoothings of the (coordinate-wise) max function in $R^{d}$ in the infinity norm. The LogSumExp function $f (x) = ln (\sum_{i}^{d} exp (x_{i}))$ provides a c…

math.OC2025

The Optimal Smoothings of Sublinear Functions and Convex Cones

Thabo Samakhoana, Benjamin Grimmer

This paper considers the problem of smoothing convex functions and sets, seeking the nearest smooth convex function or set to a given one. For convex cones and sublinear functions,…