Geodesic
Inexact and Accelerated Proximal Point Algorithms
Journal of convex analysis, Tome 19 (2012) no. 4, pp. 1167-1192.

Voir la notice de l'article provenant de la source Heldermann Verlag

We present inexact accelerated proximal point algorithms for minimizing a proper lower semicontinuous and convex function. We carry on a convergence analysis under different types of errors in the evaluation of the proximity operator, and we provide corresponding convergence rates for the objective function values. The proof relies on a generalization of the strategy proposed by O. Güler ["New proximal point algorithms for convex minimization", SIAM J. Optimization 2(4) (1992) 649--664] for generating estimate sequences according to the definition of Nesterov, and is based on the concept of ε-subdifferential. We show that the convergence rate of the exact accelerated algorithm 1/k2 can be recovered by constraining the errors to be of a certain type.
Classification : 90C25, 49D37, 65K10
Mots-clés : Accelerated proximal point algorithms, global convergence rates, approximation criteria 
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     author = {S. Salzo and S. Villa},
     title = {Inexact and {Accelerated} {Proximal} {Point} {Algorithms}},
     journal = {Journal of convex analysis},
     pages = {1167--1192},
     publisher = {mathdoc},
     volume = {19},
     number = {4},
     year = {2012},
     url = {http://geodesic.mathdoc.fr/item/JCA_2012_19_4_JCA_2012_19_4_a15/}
}
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S. Salzo; S. Villa. Inexact and Accelerated Proximal Point Algorithms. Journal of convex analysis, Tome 19 (2012) no. 4, pp. 1167-1192. http://geodesic.mathdoc.fr/item/JCA_2012_19_4_JCA_2012_19_4_a15/