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Set-valued convex compositions
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DOI：10.1007/s00186-026-00922-w.png)
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Abstract
En 中文
We study the composition of two set-valued functions defined on locally convex topological linear spaces. We assume that these functions map into certain complete lattices of sets that have been used to establish a conjugation theory for set-valued functions in the literature. Our main result is a formula for the conjugate of the composition in terms of the conjugates of the ingredient functions. As a special case, when the composition is proper and has further regularity, our formula yields a dual representation for the composition. The proof of the main result uses Lagrange duality and minimax theory in a nontrivial way.
Keywords:
Complete lattice
Set-valued function
Convex function
Composition
Conjugation
Fenchel-Moreau theorem
Journal
M
IF:
1.2
Papers:
24
Citations:
0