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- W3100646737 abstract "A pointed convex cone in a Hilbert space naturally induces a partial order, and further a notion of nondecreasingness for functions. We consider extended real-valued functions defined on the cone. Monotone conjugates for these functions can be defined in an analogous way to the standard convex conjugate. The only difference is that the supremum is taken over the cone instead of the entire space. The main result is the corresponding Fenchel-Moreau biconjugation identity for proper, convex, lower semicontinuous and nondecreasing functions provided the cone is perfect. Essentially, a cone is called perfect if it is self-dual and each face of the cone is self-dual in its own span. When the cone is merely self-dual, the Fenchel-Moreau identity still holds for such a function under an additional assumption that its domain has nonempty interior." @default.
- W3100646737 created "2020-11-23" @default.
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- W3100646737 date "2020-11-13" @default.
- W3100646737 modified "2023-10-01" @default.
- W3100646737 title "Fenchel-Moreau identities on self-dual cones" @default.
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