The max-$k$-sum of a set of real scalars is the maximum sum of a subset of size $k$, or alternatively the sum of the $k$ largest elements. We study two extensions: First, we show how to obtain smooth approximations to functions that are pointwise max-$k$-sums of smooth functions. Second, we discuss how the max-$k$-sum can be defined on vectors in a finite-dimensional real vector space ordered by a closed convex cone.

## Citation

manuscript, School of Operations Research and Information Engineering, Cornell University, Ithaca, NY, September 2016 To appear in Mathematical Programming. The final publication is available at link.springer.com at https://link.springer.com/article/10.1007/s10107-017-1201-0