Sequential and exact formulae for the subdifferential of nonconvex integral functionals
Rafael Corrêa, Abderrahim Hantoute, Pedro Pérez-Aros · arXiv (Cornell University) · 2018
This work concerns the study of the subdifferential of the integral functional $$ E_f(x)=\int_{T} f(t,x)dμ(t), $$ where $f$ is a (not necessarily convex) normal integrand, $({T},\mathcal{A},μ)$ is a $σ$-finite measure space, while the decision variables vary in a separable Asplund space. First, using techniques of variational analysis we establish sequential approximate formulae for the Fréchet subdifferential of $E_f$. Secondly, we introduce a Lipschitz-like condition, which allows us to give an upper-estimation for the limiting subdifferential of $E_{f}$ even when this functional is non-Lipschitz.