### Abstract

We consider the CQ algorithm, with choice of steps introduced by Yang (J. Math. Anal. Appl. 302 (2005), 166-179), for solving the split feasibility problem (SFP): Find x Ie{cyrillic, ukrainian} C such that Ax Ie{cyrillic, ukrainian} Q, where C and Q are nonempty closed convex subsets of ℝ^{n} and ℝ^{m}, respectively, and A is an m × n matrix. We convert the SFP to an equivalent convexly constrained nonlinear system of finding a zero in C of an inverse strongly monotone operator, which enables us to introduce new convergent iterative algorithms. Two restrictive conditions of Yang (i.e., the boundedness of Q and the full column rank of A) are completely removed in our new algorithms.

Original language | English (US) |
---|---|

Pages (from-to) | 489-496 |

Number of pages | 8 |

Journal | Fixed Point Theory |

Volume | 12 |

Issue number | 2 |

State | Published - 2011 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics
- Computational Mathematics

### Cite this

*Fixed Point Theory*,

*12*(2), 489-496.

}

*Fixed Point Theory*, vol. 12, no. 2, pp. 489-496.

**Choices of variable steps of the CQ algorithm for the split feasibility problem.** / Wang, Fenghui; Xu, Hong Kun; Su, Meng.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Choices of variable steps of the CQ algorithm for the split feasibility problem

AU - Wang, Fenghui

AU - Xu, Hong Kun

AU - Su, Meng

PY - 2011

Y1 - 2011

N2 - We consider the CQ algorithm, with choice of steps introduced by Yang (J. Math. Anal. Appl. 302 (2005), 166-179), for solving the split feasibility problem (SFP): Find x Ie{cyrillic, ukrainian} C such that Ax Ie{cyrillic, ukrainian} Q, where C and Q are nonempty closed convex subsets of ℝn and ℝm, respectively, and A is an m × n matrix. We convert the SFP to an equivalent convexly constrained nonlinear system of finding a zero in C of an inverse strongly monotone operator, which enables us to introduce new convergent iterative algorithms. Two restrictive conditions of Yang (i.e., the boundedness of Q and the full column rank of A) are completely removed in our new algorithms.

AB - We consider the CQ algorithm, with choice of steps introduced by Yang (J. Math. Anal. Appl. 302 (2005), 166-179), for solving the split feasibility problem (SFP): Find x Ie{cyrillic, ukrainian} C such that Ax Ie{cyrillic, ukrainian} Q, where C and Q are nonempty closed convex subsets of ℝn and ℝm, respectively, and A is an m × n matrix. We convert the SFP to an equivalent convexly constrained nonlinear system of finding a zero in C of an inverse strongly monotone operator, which enables us to introduce new convergent iterative algorithms. Two restrictive conditions of Yang (i.e., the boundedness of Q and the full column rank of A) are completely removed in our new algorithms.

UR - http://www.scopus.com/inward/record.url?scp=80055087289&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80055087289&partnerID=8YFLogxK

M3 - Article

VL - 12

SP - 489

EP - 496

JO - Fixed Point Theory

JF - Fixed Point Theory

SN - 1583-5022

IS - 2

ER -