Geodesic
Quantitative Results on the Multi-Parameters Proximal Point Algorithm
Journal of convex analysis, Tome 28 (2021) no. 3, pp. 729-75
Cet article a éte moissonné depuis la source Heldermann Verlag

Voir la notice de l'article

We give a quantitative analysis of a theorem due to Fenghui Wang and Huanhuan Cui concerning the convergence of a multi-parametric version of the proximal point algorithm. Wang and Cui's result ensures the convergence of the algorithm to a zero of the operator. Our quantitative analysis provides explicit bounds on the metastability (in the sense of Terence Tao) for the convergence and the asymptotic regularity of the iteration. Moreover, our analysis bypasses the need of sequential weak compactness and only requires a weak form of the metric projection argument.
Classification : 47H09, 47N10, 03F10, 46S30
Mots-clés : Maximal monotone operator, proximal point algorithm, metastability, asymptotic regularity, proof mining 
@article{JCA_2021_28_3_JCA_2021_28_3_a0,
     author = {B. Dinis and P. Pinto},
     title = {Quantitative {Results} on the {Multi-Parameters} {Proximal} {Point} {Algorithm}},
     journal = {Journal of convex analysis},
     pages = {729--75},
     year = {2021},
     volume = {28},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2021_28_3_JCA_2021_28_3_a0/}
}
TY  - JOUR
AU  - B. Dinis
AU  - P. Pinto
TI  - Quantitative Results on the Multi-Parameters Proximal Point Algorithm
JO  - Journal of convex analysis
PY  - 2021
SP  - 729
EP  - 75
VL  - 28
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/JCA_2021_28_3_JCA_2021_28_3_a0/
ID  - JCA_2021_28_3_JCA_2021_28_3_a0
ER  - 
%0 Journal Article
%A B. Dinis
%A P. Pinto
%T Quantitative Results on the Multi-Parameters Proximal Point Algorithm
%J Journal of convex analysis
%D 2021
%P 729-75
%V 28
%N 3
%U http://geodesic.mathdoc.fr/item/JCA_2021_28_3_JCA_2021_28_3_a0/
%F JCA_2021_28_3_JCA_2021_28_3_a0
B. Dinis; P. Pinto. Quantitative Results on the Multi-Parameters Proximal Point Algorithm. Journal of convex analysis, Tome 28 (2021) no. 3, pp. 729-75. http://geodesic.mathdoc.fr/item/JCA_2021_28_3_JCA_2021_28_3_a0/