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- W1889804802 abstract "We consider convex sets and functions over idempotent semifields, like the max-plus semifield. We show that if $K$ is a conditionally complete idempotent semifield, with completion $bar{K}$, a convex function $K^ntobar{K}$ which is lower semi-continuous in the order topology is the upper hull of supporting functions defined as residuated differences of affine functions. This result is proved using a separation theorem for closed convex subsets of $K^n$, which extends earlier results of Zimmermann, Samborski, and Shpiz." @default.
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- W1889804802 date "2005-01-01" @default.
- W1889804802 modified "2023-09-25" @default.
- W1889804802 title "Max-plus convex sets and functions" @default.
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- W1889804802 doi "https://doi.org/10.1090/conm/377/06987" @default.
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