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

Antonio Boccuto

doi:10.2478/tmmp-2021-0010

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

Tatra Mountains Mathematical Publications

Volume 78 (2021): Issue 1 (October 2021)

By: Antonio Boccuto

Open Access

|Jan 2022

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.

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Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2021-0010 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 139 - 156

Submitted on: Dec 1, 2020

Published on: Jan 1, 2022

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

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,

Related subjects:

© 2022 Antonio Boccuto, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 78 (2021): Issue 1 (October 2021)