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pro vyhledávání: '"Ferrera, Juan"'
Autor:
Ferrera, Juan, Gil, Javier Gómez
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 differentiability. More precisely, we require Lipschitz continuity, and c
Externí odkaz:
http://arxiv.org/abs/2403.08470
In this paper we prove that every locally minimizing curve with constant speed in a prox-regular subset of a Riemannian manifold is a weak geodesic. Moreover, it is shown that under certain assumptions, every weak geodesic is locally minimizing. Furt
Externí odkaz:
http://arxiv.org/abs/2311.13256
We give a definition of weak geodesics on prox-regular subsets of Riemannian manifolds as continuous curves with some weak regularities. Then obtaining a suitable Lipschitz constant of the projection map, we characterize weak geodesics on a prox-regu
Externí odkaz:
http://arxiv.org/abs/2205.08757
Autor:
Ferrera, Juan
In this note we define a $C^1$ function $F:[0,M]^2\to [0,2]$ that satisfies that its set of critical values has positive measure. This function provides an example, easier than those that usually appear in the literature, of how the order of differen
Externí odkaz:
http://arxiv.org/abs/2202.08000
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 sequence of weights does not belong to $c_0$.
Comment: 14 pages
Comment: 14 pages
Externí odkaz:
http://arxiv.org/abs/1909.05545
Autor:
Ferrera, Juan, Gil, Javier Gómez
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 $\mathbb{R}$. In this paper we characterize its superdifferential.
Co
Co
Externí odkaz:
http://arxiv.org/abs/1906.10192
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 infinite derivative has Hausdorff dimension one and Lebesgue measure zero.
Externí odkaz:
http://arxiv.org/abs/1903.11631
Akademický článek
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Let $E$ be an arbitrary subset of a Banach space $X$, $f: E \rightarrow \mathbb{R}$ be a function, and $G:E \rightrightarrows X^*$ be a set-valued mapping. We give necessary and sufficient conditions on $f, G$ for the existence of a continuous convex
Externí odkaz:
http://arxiv.org/abs/1811.05538