The proximalpointalgorithm (PPA) is a classical method for finding zeros of maximal monotone operators. It is known that the algorithm only has weak convergence in a general Hilbert space. Recently, Wang, Wang and X...
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The proximalpointalgorithm (PPA) is a classical method for finding zeros of maximal monotone operators. It is known that the algorithm only has weak convergence in a general Hilbert space. Recently, Wang, Wang and Xu proposed two modifications of the PPA and established strong convergence theorems on these two algorithms. However, these two convergence theorems exclude an important case, namely, the over-relaxed case. In this paper, we extend the above convergence theorems from under-relaxed case to the over-relaxed case, which in turn improve the performance of these two algorithms. Preliminary numerical experiments show that the algorithm with over-relaxed parameter performs better than that with under-relaxed parameter.
The proximalpointalgorithm plays an important role in finding zeros of maximal monotone operators. It has however only weak convergence in the infinite-dimensional setting. In the present paper, we provide two contr...
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The proximalpointalgorithm plays an important role in finding zeros of maximal monotone operators. It has however only weak convergence in the infinite-dimensional setting. In the present paper, we provide two contraction-proximal point algorithms. The strong convergence of the two algorithms is proved under two different accuracy criteria on the errors. A new technique of argument is used, and this makes sure that our conditions, which are sufficient for the strong convergence of the algorithms, are weaker than those used by several other authors.
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