Convergence of a hybrid projection-proximal point algorithm coupled with approximation methods in convex optimization

Felipe Alvarez*, Miguel Carrasco, Karine Pichard

*Autor correspondiente de este trabajo

Resultado de la investigación: Contribución a una revistaArtículorevisión exhaustiva

3 Citas (Scopus)

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 originalInglés
Páginas (desde-hasta)966-984
Número de páginas19
PublicaciónMathematics of Operations Research
Volumen30
N.º4
DOI
EstadoPublicada - nov. 2005
Publicado de forma externa

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