Approximating Solutions of Maximal Monotone Operators in Hilbert Spaces |
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Authors: | Shoji Kamimura Wataru Takahashi |
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Affiliation: | Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Ohokayama, Meguro-ku, Tokyo, 152-8552, Japanf1 |
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Abstract: | Let H be a real Hilbert space and let T: H→2H be a maximal monotone operator. In this paper, we first introduce two algorithms of approximating solutions of maximal monotone operators. One of them is to generate a strongly convergent sequence with limit vT−10. The other is to discuss the weak convergence of the proximal point algorithm. Next, using these results, we consider the problem of finding a minimizer of a convex function. Our methods are motivated by Halpern's iteration and Mann's iteration. |
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Keywords: | maximal monotone operator resolvent proximal point algorithm iteration strong convergence weak convergence |
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