Geodesic
Minimization problem of proximal point algorithm in complete cat(0) spaces
Filomat, Tome 36 (2022) no. 18, p. 6289

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DOI

In this paper a proximal point algorithm for a convex function is considered in complete CAT(0) spaces. We introduce a necessary and sufficient condition for the set of minimizers of the function to be nonempty, and by showing that in this case, this iterative sequence converges strongly to the metric projection of some point onto the set of minimizers of the function.
DOI : 10.2298/FIL2218289M
Classification : 47H04, 47H05, 26B25, 26E25, 90C33, 47H10
Keywords: Convex minimization problem, Proximal point algorithm, Nonexpansive mapping, Resolvent operator 
Sirous Moradi; Mohsen Tahernia. Minimization problem of proximal point algorithm in complete cat(0) spaces. Filomat, Tome 36 (2022) no. 18, p. 6289 . doi: 10.2298/FIL2218289M
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     title = {Minimization problem of proximal point algorithm in complete cat(0) spaces},
     journal = {Filomat},
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     year = {2022},
     volume = {36},
     number = {18},
     doi = {10.2298/FIL2218289M},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2218289M/}
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