A contraction proximal point algorithm with two monotone operators |
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Authors: | Oganeditse A Boikanyo Gheorghe Moroşanu |
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Institution: | 1. Department of Mathematics, University of Botswana, Private Bag 00704, Gaborone, Botswana;2. Department of Mathematics and its Applications, Central European University, Nador u. 9, H-1051 Budapest, Hungary |
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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. |
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Keywords: | 47J25 47H05 47H09 |
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