In this paper, some ideas for the numerical realization of the hybrid proximal projection algorithm from Solodov and Svaiter [22] are presented. An example is given which shows that this hybrid algorithm does not generate a Fejér-monotone sequence. Further, a strategy is suggested for the computation of inexact solutions of the auxiliary problems with a certain tolerance. For that purpose, ε-subdifferentials of the auxiliary functions and the bundle trust region method from Schramm and Zowe [20] are used. Finally, some numerical results for non-smooth convex optimization problems are given which compare the hybrid algorithm to the inexact proximal point method from Rockafellar [17].
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1076,
author = {Christina Jager},
title = {Numerical considerations of a hybrid proximal projection algorithm for solving variational inequalities},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
volume = {27},
year = {2007},
pages = {51-69},
zbl = {1156.47054},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1076}
}
Christina Jager. Numerical considerations of a hybrid proximal projection algorithm for solving variational inequalities. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 27 (2007) pp. 51-69. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1076/
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