### Abstract

It is a known fact that the method of alternating projections introduced long ago by von Neumann fails to converge strongly for two arbitrary nonempty, closed and convex subsets of a real Hilbert space. In this paper, a new iterative process for finding common zeros of two maximal monotone operators is introduced and strong convergence results associated with it are proved. If the two operators are subdifferentials of indicator functions, this new algorithm coincides with the old method of alternating projections. Several other important algorithms, such as the contraction proximal point algorithm, occur as special cases of our algorithm. Hence our main results generalize and unify many results that occur in the literature.

Original language | English |
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Pages (from-to) | 5686-5692 |

Number of pages | 7 |

Journal | Nonlinear Analysis, Theory, Methods and Applications |

Volume | 75 |

Issue number | 14 |

DOIs | |

Publication status | Published - Sep 1 2012 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

### Cite this

*Nonlinear Analysis, Theory, Methods and Applications*,

*75*(14), 5686-5692. https://doi.org/10.1016/j.na.2012.05.016

}

*Nonlinear Analysis, Theory, Methods and Applications*, vol. 75, no. 14, pp. 5686-5692. https://doi.org/10.1016/j.na.2012.05.016

**A contraction proximal point algorithm with two monotone operators.** / Boikanyo, Oganeditse A.; Moroşanu, Gheorghe.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A contraction proximal point algorithm with two monotone operators

AU - Boikanyo, Oganeditse A.

AU - Moroşanu, Gheorghe

PY - 2012/9/1

Y1 - 2012/9/1

N2 - It is a known fact that the method of alternating projections introduced long ago by von Neumann fails to converge strongly for two arbitrary nonempty, closed and convex subsets of a real Hilbert space. In this paper, a new iterative process for finding common zeros of two maximal monotone operators is introduced and strong convergence results associated with it are proved. If the two operators are subdifferentials of indicator functions, this new algorithm coincides with the old method of alternating projections. Several other important algorithms, such as the contraction proximal point algorithm, occur as special cases of our algorithm. Hence our main results generalize and unify many results that occur in the literature.

AB - It is a known fact that the method of alternating projections introduced long ago by von Neumann fails to converge strongly for two arbitrary nonempty, closed and convex subsets of a real Hilbert space. In this paper, a new iterative process for finding common zeros of two maximal monotone operators is introduced and strong convergence results associated with it are proved. If the two operators are subdifferentials of indicator functions, this new algorithm coincides with the old method of alternating projections. Several other important algorithms, such as the contraction proximal point algorithm, occur as special cases of our algorithm. Hence our main results generalize and unify many results that occur in the literature.

UR - http://www.scopus.com/inward/record.url?scp=84862994785&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84862994785&partnerID=8YFLogxK

U2 - 10.1016/j.na.2012.05.016

DO - 10.1016/j.na.2012.05.016

M3 - Article

VL - 75

SP - 5686

EP - 5692

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

IS - 14

ER -