Marino, Giuseppe; Xu, Hong-Kun Convergence of generalized proximal point algorithms. (English) Zbl 1095.90115 Commun. Pure Appl. Anal. 3, No. 4, 791-808 (2004). Summary: Weak and strong convergence for some generalized proximal point algorithms are proved. These algorithms include the Eckstein and Bertsekas generalized proximal point algorithm, a contraction-proximal point algorithm, and inexact proximal point algorithms. Convergence rate is also considered. Cited in 101 Documents MSC: 90C48 Programming in abstract spaces 49J40 Variational inequalities 47J20 Variational and other types of inequalities involving nonlinear operators (general) 65J15 Numerical solutions to equations with nonlinear operators Keywords:maximal monotone operator; resolvent identity; nonexpansive mapping; projection; generalized proximal point algorithm; contraction-proximal point algorithm; inexact proximal point algorithms PDFBibTeX XMLCite \textit{G. Marino} and \textit{H.-K. Xu}, Commun. Pure Appl. Anal. 3, No. 4, 791--808 (2004; Zbl 1095.90115) Full Text: DOI