Abderrahim Hantoute

TL;DR: A rule to calculate the subdifferential set of the pointwise supremum of an arbitrary family of convex functions defined on a real locally convex topological vector space is provided.

Abstract: We give a simple proof of the so-called Potential well theorem of Ioffe and Schwartzman, estimating the size of the potential well associated with a local minimum of a continuous functional defined on a complete metric space. Applications to the homotopical stability of an isolated local minimum and to an abstract bifurcation result, as in Ioffe and Schwartzman, are described. We also establish a result on homotopical stability of arbitrary isolated critical points of continuous functionals, thus extending a result of Chang.

TL;DR: Canovas et al. as mentioned in this paper showed that ENC also entails high stability for the minimal subsets of indices involved in the KKT conditions, yielding a nice behavior not only for the optimal set mapping, but also for its inverse.

TL;DR: In this paper, the authors established new rules for the calculus of the subdifferential mapping of the sum of two convex functions, and gave an application to derive asymptotic optimality conditions for convex optimization.

TL;DR: In this paper, the authors provide subdifferential formulae of probability functions in the case of Gaussian distributions for possibly infinite-dimensional decision variables and nonsmooth (locally Lipschitzian) input data.