A viscosity solution approach to regularity properties of the optimal value function
Analysis of PDEs
2020-12-08 v1
Abstract
In this paper we analyze the optimal value function associated to a general parametric optimization problems via the theory of viscosity solutions. The novelty is that we obtain regularity properties of by showing that it is a viscosity solution to a set of first-order equations. As a consequence, in Banach spaces, we provide sufficient conditions for local and global Lipschitz properties of . We also derive, in finite dimensions, conditions for optimality through a comparison principle. Finally, we study the relationship between viscosity and Clarke generalized solutions to get further differentiability properties of in Euclidean spaces.
Cite
@article{arxiv.2012.03401,
title = {A viscosity solution approach to regularity properties of the optimal value function},
author = {Ochoa Pablo and Virginia N. Vera de Serio},
journal= {arXiv preprint arXiv:2012.03401},
year = {2020}
}