<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>We give some versions of Hahn-Banach, sandwich, duality, Moreau--Rockafellar-type theorems, optimality conditions and a formula for the subdifferential of composite functions for order continuous vector lattice-valued operators, invariant or equivariant with respect to a fixed group <italic>G</italic> of homomorphisms. As applications to optimization problems with both convex and linear constraints, we present some Farkas and Kuhn-Tucker-type results.</p>
</abstract>

We give some versions of Hahn-Banach, sandwich, duality, Moreau--Rockafellar-type theorems, optimality conditions and a formula for the subdifferential of composite functions for order continuous vector lattice-valued operators, invariant or equivariant with respect to a fixed group G of homomorphisms. As applications to optimization problems with both convex and linear constraints, we present some Farkas and Kuhn-Tucker-type results.

Hahn-Banach-Type Theorems and Subdifferentials for Invariant and Equivariant Order Continuous Vector Lattice-Valued Operators with Applications to Optimization

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

We give some versions of Hahn-Banach, sandwich, duality, Moreau--Rockafellar-type theorems, optimality conditions and a formula for the subdifferential of...

Hahn-Banach-Type Theorems and Subdifferentials for Invariant and Equivariant Order Continuous Vector Lattice-Valued Operators with Applications to Optimization

Published Online: Jan 01, 2022

Page range: 139 - 156

Received: Dec 01, 2020

DOI: https://doi.org/10.2478/tmmp-2021-0010

Keywords
vector lattice, order bounded functional, order continuous functional, amenability, Hahn-Banach theorem, sandwich theorem, Fenchel duality theorem, subgradient, subdifferential of composite functions, optimality condition, Moreau-Rockafellar formula, Farkas theorem, Kuhn-Tucker theorem

© 2021 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Hahn-Banach-Type Theorems and Subdifferentials for Invariant and Equivariant Order Continuous Vector Lattice-Valued Operators with Applications to Optimization

Published Online: Jan 01, 2022

Page range: 139 - 156

Received: Dec 01, 2020

DOI: https://doi.org/10.2478/tmmp-2021-0010

Keywordsvector lattice, order bounded functional, order continuous functional, amenability, Hahn-Banach theorem, sandwich theorem, Fenchel duality theorem, subgradient, subdifferential of composite functions, optimality condition, Moreau-Rockafellar formula, Farkas theorem, Kuhn-Tucker theorem

© 2021 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
vector lattice, order bounded functional, order continuous functional, amenability, Hahn-Banach theorem, sandwich theorem, Fenchel duality theorem, subgradient, subdifferential of composite functions, optimality condition, Moreau-Rockafellar formula, Farkas theorem, Kuhn-Tucker theorem