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An iterative algorithm for approximating convex minimization problem. (English) Zbl 1121.65071
The authors propose a new algorithm for the convex minimization problem, without assuming any type of commutativity properties on an infinite family of nonexpansive mappings. The first two sections present an overview of the problem and its applications as well as some useful background information and relevant known theorems. In the third and last section, the main result of this short article is presented, in the form of a theorem that relates to the strong convergence of the proposed algorithm, which is the unique minimizer of the quadratic function over the set of fixed points.
MSC:
65K05Mathematical programming (numerical methods)
90C25Convex programming