Iterative algorithms based on the hybrid steepest descent method for the split feasibility problem

Volume 9, Issue 6, pp 4214--4225 http://dx.doi.org/10.22436/jnsa.009.06.63

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Authors

Jong Soo Jung - Department of Mathematics, Dong-A University, Busan 49315, Korea.

Abstract

In this paper, we introduce two iterative algorithms based on the hybrid steepest descent method for solving the split feasibility problem. We establish results on the strong convergence of the sequences generated by the proposed algorithms to a solution of the split feasibility problem, which is a solution of a certain variational inequality. In particular, the minimum norm solution of the split feasibility problem is obtained.

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Keywords

• Split feasibility problem
• nonexpansive mapping
• variational inequality
• minimum-norm
• projection
• bounded linear operator
• \(\rho\)-Lipschitzian
• \(\eta\)-strongly monotone operator.

MSC

•  47J20
•  47J25
•  47J05
•  47H09
•  47H10
•  47H05

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