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Zbl 1071.47062
Kohsaka, Fumiaki; Takahashi, Wataru
Iterative scheme for finding a common point of infinitely many convex sets in a Banach space. (English)
[J] J. Nonlinear Convex Anal. 5, No. 3, 407-414 (2004). ISSN 1345-4773; ISSN 1880-5221/e

Based on previous work by Kamimura and Takahashi, and Nakajo and Takahashi, the authors study the convergence of an iterative scheme for finding a common point of a countable infinite family of closed convex subsets of a uniformly convex Banach space by using the hybrid method in mathematical programming. They prove that the sequence converges strongly to an element of the intersection set. Their results are applied to a convex minimization problem.
[Edward Prempeh (Kumasi)]

MSC 2000:: *47J25 Methods for solving nonlinear operator equations (general)
90C25 Convex programming

Keywords: convex feasibility problem; convex minimization problem; hybrid method; uniformly convex Banach space

Cited in: Zbl 1201.49033

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