2 citations · 3 across the 4 of their papers we have counts for
5 papers
Convergence of ADAM for Lipschitz Objective Functions
Juan Ferrera, Javier Gómez Gil
The aim of this paper is to prove the exponential convergence, local and global, of Adam algorithm under precise conditions on the parameters, when the objective function lacks dif…
A characterization of the nowhere differentiable functions of the Generalized Takagi Class
Juan Ferrera, Javier Gómez Gil, Jesús Llorente
In this paper, we prove that for some Generalized Takagi Classes, in particular for the Takagi-Van der Waerden Class, the functions are nowhere differentiable if, and only if, the…
Superdifferential of the Takagi function
Juan Ferrera, Javier Gómez Gil
The Takagi function is a classical example of a continuous nowhere differentiable function. It has empty subdifferential except in a countable set where its subdifferential is $\ma…
Infinite derivatives of the Takagi-Van der Waerden functions
Juan Ferrera, Javier Gómez Gil, Jesús Llorente
In this paper we characterize the set of points where the lateral derivatives of the Takagi-Van der Waerden functions are infinite. We also prove that the set of points with infini…
Non approximate derivability of the Takagi function
Juan Ferrera, Javier Gómez Gil
The Takagi function is a classical example of a continuous nowhere differentiable function. In this paper we prove that it is nowhere approximately derivable.