On max-k-sums

• 成果类型: Article
• 署名作者: Todd, Michael J.
• 署名单位: Cornell University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-017-1201-0
• 发表日期: 2018
• 页码: 489-517
• 关键词: jordan algebras; matrix

摘要

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.