Resumen
In order to minimize a closed convex function that is approximated by a sequence of better behaved functions, we investigate the global convergence of a general hybrid iterative algorithm, which consists of an inexact relaxed proximal point step followed by a suitable orthogonal projection onto a hyperplane. The latter permits to consider a fixed relative error criterion for the proximal step. We provide various sets of conditions ensuring the global convergence of this algorithm. The analysis is valid for nonsmooth data in infinite-dimensional Hilbert spaces. Some examples are presented, focusing on penalty/barrier methods in convex programming. We also show that some results can be adapted to the zero-finding problem for a maximal monotone operator.
Idioma original | Inglés |
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Páginas (desde-hasta) | 966-984 |
Número de páginas | 19 |
Publicación | Mathematics of Operations Research |
Volumen | 30 |
N.º | 4 |
DOI | |
Estado | Publicada - nov. 2005 |
Publicado de forma externa | Sí |