Max-plus Convex Sets and Functions
نویسندگان
چکیده
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 K̄, a convex function Kn → K̄ 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 Kn, which extends earlier results of Zimmermann, Samborski, and Shpiz.
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