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Iterative Algorithms for Nonlinear Operators
Author(s) -
Xu Hong-Kun
Publication year - 2002
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610702003332
Subject(s) - monotone polygon , convergence (economics) , mathematics , algorithm , minification , quadratic equation , iterative method , nonlinear system , point (geometry) , mathematical optimization , physics , quantum mechanics , geometry , economics , economic growth
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.