Abstract
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.
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Acknowledgements
The author would like to thank Gena Samorodnitsky, Leonid Faybusovich, Rob Freund, Arkadi Nemirovskii, and Yurii Nesterov for very helpful conversations.
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Todd, M.J. On max-k-sums. Math. Program. 171, 489–517 (2018). https://doi.org/10.1007/s10107-017-1201-0
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DOI: https://doi.org/10.1007/s10107-017-1201-0