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An iterative algorithm of solution for quadratic minimization problem in Hilbert spaces. (English) Zbl 1189.65126

Summary: The purpose of this paper is to introduce an iterative algorithm for finding a solution of quadratic minimization problem in the set of fixed points of a nonexpansive mapping and to prove a strong convergence theorem of the solution for quadratic minimization problem. The result of this article improves and extends the result of G. Marino and H. K. Xu [J. Math. Anal. Appl. 318, No. 1, 43–52 (2006; Zbl 1095.47038)] and some others.

MSC:

65K05 Numerical mathematical programming methods
90C20 Quadratic programming
90C48 Programming in abstract spaces
47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H10 Fixed-point theorems

Citations:

Zbl 1095.47038
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References:

[1] doi:10.1016/j.jmaa.2005.05.028 · Zbl 1095.47038 · doi:10.1016/j.jmaa.2005.05.028
[2] doi:10.1023/A:1023073621589 · Zbl 1043.90063 · doi:10.1023/A:1023073621589
[3] doi:10.1155/FPTA.2005.103 · Zbl 1123.47308 · doi:10.1155/FPTA.2005.103
[4] doi:10.1016/j.jmaa.2004.11.017 · Zbl 1068.47085 · doi:10.1016/j.jmaa.2004.11.017
[6] doi:10.1112/S0024610702003332 · Zbl 1013.47032 · doi:10.1112/S0024610702003332
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