Algorithms for approximating minimization problems in Hilbert spaces

Algorithms for approximating minimization problems in Hilbert spaces

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Article ID: iaor20114473
Volume: 235
Issue: 12
Start Page Number: 3515
End Page Number: 3526
Publication Date: Apr 2011
Journal: Journal of Computational and Applied Mathematics
Authors: , ,
Keywords: heuristics
Abstract:

In this paper, we study the following minimization problem min x F i x ( S ) Ω μ 2 B x , x + 1 2 x 2 h ( x ) , equ1 where B equ2 is a bounded linear operator, μ 0 equ3 is some constant, h equ4 is a potential function for γ ¯ f equ5, F i x ( T ) equ6 is the set of fixed points of nonexpansive mapping S equ7 and Ω equ8 is the solution set of an equilibrium problem. This paper introduces two new algorithms (one implicit and one explicit) that can be used to find the solution of the above minimization problem.

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