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Journal of the London Mathematical Society 2002 66(1):240-256; doi:10.1112/S0024610702003332
© 2002 by London Mathematical Society
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© The London Mathematical Society

Iterative Algorithms for Nonlinear Operators

Hong-Kun Xu

Department of Mathematics, University of Durban–Westville Private Bag X54001, Durban 4000, South Africa, hkxu{at}pixie.udw.ac.za

Received 10 May 2001. Revision received 10 October 2001.

Iterative algorithms for nonexpansive mappings and maximal monotone operators are investigated. Strong convergence theorems are proved for nonexpansive mappings, including an improvement of a result of Lions. A modification of Rockafellar’s proximal point algorithm is obtained and proved to be always strongly convergent. The ideas of these algorithms are applied to solve a quadratic minimization problem.


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