Convergence of generalized proximal point algorithms

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December 2004, 3(4): 791-808. doi: 10.3934/cpaa.2004.3.791

Convergence of generalized proximal point algorithms

1.	Dipartimento di Matematica, Universita della Calabria, 87036 Arcavacata di Rende (Cs), Italy
2.	School of Mathematical Sciences, University of KwaZulu-Natal, Westville Campus, Private Bag X54001, Durban 4000, South Africa

Received January 2004 Revised July 2004 Published September 2004

Abstract
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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.

Keywords: inexact) proximal point algorithm, nonexpansive mapping, Maximal monotone operator, resolvent identity, projection., generalized (contraction-.

Mathematics Subject Classification: 49J40, 47J20, 65J1.

Citation: Giuseppe Marino, Hong-Kun Xu. Convergence of generalized proximal point algorithms. Communications on Pure & Applied Analysis, 2004, 3 (4) : 791-808. doi: 10.3934/cpaa.2004.3.791

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