American Institute of Mathematical Sciences

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

Convergence of generalized proximal point algorithms

Giuseppe Marino 1, and  Hong-Kun Xu 2,

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

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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