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 |
|---|---|
| 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
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A contraction proximal point algorithm with two monotone operators. / Boikanyo, Oganeditse A.; Moroşanu, Gheorghe.
In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 75, No. 14, 01.09.2012, p. 5686-5692.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 -