Calmness of linear programs under perturbations of all data: characterization and modulus

This paper provides operative point-based formulas (only involving the nominal data, and not data in a neighborhood) for computing or estimating the calmness modulus of the optimal set (argmin) mapping in linear optimization under uniqueness of nominal optimal solutions. Our analysis is developed in two different parametric settings. First, in the framework of canonical perturbations … Read more

Subdifferential of the conjugate function in general Banach spaces

We give explicit formulas for the subdifferential set of the conjugate of non necessarily convex functions defined on general Banach spaces. Even if such a subdifferential mapping takes its values in the bidual space, we show that up to a weak** closure operation it is still described by using only elements of the initial space … Read more

Integration formulas via the Legendre-Fenchel Subdifferential of nonconvex functions

Starting from explicit expressions for the subdifferential of the conjugate function, we establish in the Banach space setting some integration results for the so-called epi-pointed functions. These results use the epsilon-subdifferential and the Legendre-Fenchel subdefferential of an appropriate weak lower semicontinuous (lsc) envelope of the initial function. We apply these integration results to the construction … Read more

New formulas for the Fenchel subdifferential of the conjugate function

Following [13] we provide new formulas for the Fenchel subdifferential of the conjugate of functions defined on locally convex spaces. In particular, this allows deriving expressions for the minimizers set of the lower semicontinuous convex hull of such functions. These formulas are written by means of primal objects related to the subdifferential of the initial … Read more

Nonsmooth Lyapunov pairs for infinite-dimensional first-order differential inclusions

The main objective of this paper is to provide new explicit criteria to characterize weak lower semi-continuous Lyapunov pairs or functions associated to first-order differential inclusions in Hilbert spaces. These inclusions are governed by a Lipschitzian perturbation of a maximally monotone operator. The dual criteria we give are expressed by the means of the proximal … Read more