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Set-valued convex compositions

Çağın Ararat

Mathematical Methods of Operations Research2026https://doi.org/10.1007/s00186-026-00922-wpreprint
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0.50

What the paper says

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.

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https://doi.org/https://doi.org/10.1007/s00186-026-00922-w

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@article{çağın2026,
  title        = {{Set-valued convex compositions}},
  author       = {Çağın Ararat},
  journal      = {Mathematical Methods of Operations Research},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1007/s00186-026-00922-w},
}

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Set-valued convex compositions

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Evidence weight

0.50

Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40

F · citation impact0.50 × 0.4 = 0.20
M · momentum0.50 × 0.15 = 0.07
V · venue signal0.50 × 0.05 = 0.03
R · text relevance †0.50 × 0.4 = 0.20

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