Geodesic
A Class of Variable Metric Decomposition Methods for Monotone Variational Inclusions
Journal of convex analysis, Tome 16 (2009) no. 3, pp. 857-88.

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

We extend the general decomposition scheme of M. V. Solodov [Optimization Methods and Software 19 (2004) 557--575], which is based on the hybrid inexact proximal point method of M. V. Solodov and B. F. Svaiter [Numerical Functional Analysis and Optimization 22 (2001) 1013--1035], to allow the use of variable metric in subproblems, along the lines described in a previous paper of the authors [SIAM Journal on Optimization 19 (2008) 240--260]. We show that the new general scheme includes as special cases the splitting method for composite mappings [see T. Pennanen, Numerical Functional Analysis and Optimization 23 (2002) 875--890] and the proximal alternating directions method [see J. Eckstein, Optimization Methods and Software 4 (1994) 75--83, and B. He, L. Z. Liao, D. Han and H. Yang, Mathematical Programming 92 (2002) 103--118] (in addition to the decomposition methods of X. Chen and M. Teboulle [Mathematical Programming 64 (1994) 81--101] and P. Tseng [SIAM Journal on Optimization 7 (1997) 951--965] that were already covered in the above-mentioned article by M. V. Solodov [Optimization Methods and Software 19 (2004) 557--575]). Apart from giving a unified insight into the decomposition methods in question and openning the possibility of using variable metric, which is a computationally important issue, this development also provides linear rate of convergence results not previously available for splitting of composite mappings and for the proximal alternating directions methods.
Mots-clés : Proximal point methods, variable metric, maximal monotone operator, variational inclusion, splitting, decomposition 
@article{JCA_2009_16_3_JCA_2009_16_3_a17,
     author = {P. A. Lotito and L. A. Parente and M. Solodov},
     title = {A {Class} of {Variable} {Metric} {Decomposition} {Methods} for {Monotone} {Variational} {Inclusions}},
     journal = {Journal of convex analysis},
     pages = {857--88},
     publisher = {mathdoc},
     volume = {16},
     number = {3},
     year = {2009},
     url = {http://geodesic.mathdoc.fr/item/JCA_2009_16_3_JCA_2009_16_3_a17/}
}
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P. A. Lotito; L. A. Parente; M. Solodov. A Class of Variable Metric Decomposition Methods for Monotone Variational Inclusions. Journal of convex analysis, Tome 16 (2009) no. 3, pp. 857-88. http://geodesic.mathdoc.fr/item/JCA_2009_16_3_JCA_2009_16_3_a17/