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Convergence of generalized proximal point algorithms. (English) Zbl 1095.90115

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:

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
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