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

Fenghui Wang, Hong Kun Xu, Meng Su

Research output: Contribution to journalArticle

9 Citations (Scopus)

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 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.

Original languageEnglish (US)
Pages (from-to)489-496
Number of pages8
JournalFixed Point Theory
Volume12
Issue number2
StatePublished - 2011

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Monotone Operator
Constrained Systems
Iterative Algorithm
Convert
Boundedness
Nonlinear Systems
Closed
Subset
Nonlinear systems
Zero

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics
  • Computational Mathematics

Cite this

Wang, Fenghui ; Xu, Hong Kun ; Su, Meng. / Choices of variable steps of the CQ algorithm for the split feasibility problem. In: Fixed Point Theory. 2011 ; Vol. 12, No. 2. pp. 489-496.
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Choices of variable steps of the CQ algorithm for the split feasibility problem. / Wang, Fenghui; Xu, Hong Kun; Su, Meng.

In: Fixed Point Theory, Vol. 12, No. 2, 2011, p. 489-496.

Research output: Contribution to journalArticle

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