Convergence of generalized proximal point algorithms

Giuseppe Marino; Hong-Kun Xu

doi:10.3934/cpaa.2004.3.791

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2004, Volume 3, Issue 4: 791-808. Doi: 10.3934/cpaa.2004.3.791

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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)
2.
School of Mathematical Sciences, University of KwaZulu-Natal, Westville Campus, Private Bag X54001, Durban 4000

Received: December 31, 2003

Revised: June 30, 2004

Published: November 2004

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Abstract

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.

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Mathematics Subject Classification: 49J40, 47J20, 65J15.

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