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Zbl 1095.90115
Marino, Giuseppe; Xu, Hong-Kun
Convergence of generalized proximal point algorithms. (English)
[J] Commun. Pure Appl. Anal. 3, No. 4, 791-808 (2004). ISSN 1534-0392; ISSN 1553-5258/e

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.

MSC 2000:: *90C48 Programming in abstract spaces
49J40 Variational methods including variational inequalities
47J20 Inequalities involving nonlinear operators
65J15 Equations with nonlinear operators (numerical methods)

Keywords: maximal monotone operator; resolvent identity; nonexpansive mapping; projection; generalized proximal point algorithm; contraction-proximal point algorithm; inexact proximal point algorithms

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Zentralblatt MATH Berlin [Germany]