MONOTONE OPERATORS AND THE PROXIMAL POINT ALGORITHM IN COMPLETE CAT(0) METRIC SPACES
2016 ◽
Vol 103
(1)
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pp. 70-90
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Keyword(s):
In this paper, we generalize monotone operators, their resolvents and the proximal point algorithm to complete CAT(0) spaces. We study some properties of monotone operators and their resolvents. We show that the sequence generated by the inexact proximal point algorithm $\unicode[STIX]{x1D6E5}$-converges to a zero of the monotone operator in complete CAT(0) spaces. A strong convergence (convergence in metric) result is also presented. Finally, we consider two important special cases of monotone operators and we prove that they satisfy the range condition (see Section 4 for the definition), which guarantees the existence of the sequence generated by the proximal point algorithm.
2010 ◽
Vol 31
(9)
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pp. 1053-1071
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Keyword(s):
2020 ◽
Vol 186
(1)
◽
pp. 134-147
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Keyword(s):
2021 ◽
Vol 31
(2)
◽
pp. 117-124
2012 ◽
Vol 194
(2)
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pp. 689-701
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1976 ◽
Vol 14
(5)
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pp. 877-898
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1999 ◽
Vol 37
(2)
◽
pp. 353-375
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2019 ◽
Vol 13
(6)
◽
pp. 247-258