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Artículo
An abstract proximal point algorithm
(Springer, 2018)
The proximal point algorithm is a widely used tool for solving a variety of convex optimization problems such as finding zeros of maximally monotone operators, fixed points of nonexpansive mappings, as well as minimizing ...
Artículo
A proof-theoretic bound extraction theorem for CAT(κ)-spaces
(Springer, 2017-06)
Starting in 2005, general logical metatheorems have been developed that guarantee the extractability of uniform effective bounds from large classes of proofs of theorems that involve abstract metric structures X. In this ...
Artículo
Quantitative results on Fejér monotone sequences
(World Scientific, 2017)
We provide in a unified way quantitative forms of strong convergence results for numerous iterative procedures which satisfy a general type of Fej´er monotonicity where the convergence uses the compactness of the underlying ...
Artículo
Effective results on nonlinear ergodic averages in CAT(κ) spaces
(Cambridge University Press, 2016-12)
In this paper we apply proof mining techniques to compute, in the setting of CAT(κ) spaces (with κ > 0), effective and highly uniform rates of asymptotic regularity and metastability for a nonlinear generalization of the ...
Artículo
Effective results on compositions of nonexpansive mappings
(Elsevier, 2014-02-15)
This paper provides uniform bounds on the asymptotic regularity for iterations associated to a finite family of nonexpansive mappings. We obtain our quantitative results in the setting of (r, δ)-convex spaces, a class ...
Artículo
Asymptotic behavior of averaged and firmly nonexpansive mappings in geodesic spaces
(Elsevier, 2013-08)
We further study averaged and firmly nonexpansive mappings in the setting of geodesic spaces with a main focus on the asymptotic behavior of their Picard iterates. We use methods of proof mining to obtain an explicit ...