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 ${\mathbb{R}}^d$ in the infinity norm. The LogSumExp function $f(x)=\ln ({\sum }_i^d\exp (x_i))$ provides a c…