Hahn-Banach-type theorems and subdifferentials for invariant and equivariant order continuous vector lattice-valued operators with applications to optimization

Year, pages: 2021, 139 - 156

We prove Hahn-Banach, sandwich and extension theorems for vector lattice-valued operators, equivariant with respect to a given group $G$ of homomorphisms. As applications and consequences, we present some Fenchel duality and separation theorems, a version of the Moreau-Rockafellar formula and some Farkas and Kuhn-Tucker-type optimization results. Finally, we prove that the obtained results are equivalent to the amenability of $G$.

Boccuto, A. 2021. Hahn-Banach-type theorems and subdifferentials for invariant and equivariant order continuous vector lattice-valued operators with applications to optimization. In Tatra Mountains Mathematical Publications, vol. 78, no.1, pp. 139-156. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2021-0010

Boccuto, A. (2021). Hahn-Banach-type theorems and subdifferentials for invariant and equivariant order continuous vector lattice-valued operators with applications to optimization. Tatra Mountains Mathematical Publications, 78(1), 139-156. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2021-0010

Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava

https://creativecommons.org/licenses/by-nc-nd/4.0/