English

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}
}