2002•Journal of the London Mathematical SocietyRequires access

Iterative Algorithms for Nonlinear Operators

Hong‐Kun Xu

Abstract

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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Key concepts: Monotone polygon, Convergence (economics), Mathematics, Algorithm, Minification, Quadratic equation, Iterative method, Nonlinear system