Integral functionals on nonseparable Banach spaces with applications
Optimization and Control
2022-08-10 v2 Functional Analysis
Probability
Abstract
In this paper, we study integral functionals defined on spaces of functions with values on general (non-separable) Banach spaces. We introduce a new class of integrands and multifunctions for which we obtain measurable selection results. Then, we provide an interchange formula between integration and infimum, which enables us to get explicit formulas for the conjugate and Clarke subdifferential of integral functionals. Applications to expected functionals from stochastic programming, optimality conditions for a calculus of variation problem and sweeping processes are given.
Cite
@article{arxiv.2208.00507,
title = {Integral functionals on nonseparable Banach spaces with applications},
author = {Juan Guillermo Garrido and Pedro Pérez-Aros and Emilio Vilches},
journal= {arXiv preprint arXiv:2208.00507},
year = {2022}
}