Value Functions and Optimality Conditions for Nonconvex Variational Problems with an Infinite Horizon in Banach Spaces
Optimization and Control
2020-02-11 v3 Functional Analysis
Abstract
We investigate the value function of an infinite horizon variational problem in the infinite-dimensional setting. Firstly, we provide an upper estimate of its Dini--Hadamard subdifferential in terms of the Clarke subdifferential of the Lipschitz continuous integrand and the Clarke normal cone to the graph of the set-valued mapping describing dynamics. Secondly, we derive a necessary condition for optimality in the form of an adjoint inclusion that grasps a connection between the Euler--Lagrange condition and the maximum principle.
Keywords
Cite
@article{arxiv.1801.00400,
title = {Value Functions and Optimality Conditions for Nonconvex Variational Problems with an Infinite Horizon in Banach Spaces},
author = {Hélène Frankowska and Nobusumi Sagara},
journal= {arXiv preprint arXiv:1801.00400},
year = {2020}
}