The strong convergence of a proximal pointalgorithm in complete CAT(0) metric spaces

References (1)

1. P. Ahmadi and H. Khatibzadeh,On the convergence of inexact proximal point algo-rithm on Hadamard manifolds, Taiwanese J. Math.18, 419–433, 2014. [2]B. Ahmadi Kakavandi,Weak topologies in complete CAT(0) metric spaces, Proc.Amer. Math. Soc.141, 1029–1039, 2013. [3]B. Ahmadi Kakavandi and M. Amini,Duality and subdifierential for convex functionson complete CAT(0) metric spaces, Nonlinear Anal.73, 3450–3455, 2010. [4]M. Bacak,Convex analysis and optimization in Hadamard spaces, De Gruyter Seriesin Nonlinear Analysis and Applications,22, De Gruyter, Berlin, 2014. [5]I.D. Berg and I.G. Nikolaev,Quasilinearization and curvature of Alexandrov spaces,Geom. Dedicata,133, 195–218, 2008. [6]H. Br ́ezis and P.L. Lions,Produits infinis de r ́esolvantes, Israel J. Math.29, 329–345,1978. [7]M. Bridson and A. Haefliger,Metric spaces of non-positive curvature,319, Springer,Berlin, 1999. [8]K.S. Brown,Buildings, Springer, New York, 1989. [9]D. Burago, Y. Burago and S. Ivanov,A course in metric geometry, Graduate Studiesin Mathematics,33American Mathematical Society, Providence, RI, 2001. [10]H. Dehghan and J. Rooin,Metric projection and convergence theorems for nonexpan-sive mappings in Hadamard spaces, arXiv: 1410.1137v1[math.FA]. [11]S. Dhompongsa and B. Panyanak,On△-convergence theorems in CAT(0) spaces,Comput. Math. Appl.56, 2572–2579, 2008. [12]B. Djafari Rouhani and H. Khatibzadeh,On the proximal point algorithm, J. Optim.Theory Appl.137, 411–417, 2008. [13]B. Djafari Rouhani and S. Moradi, Strong convergence of two proximal point algo-rithms with possible unbounded error sequences, J. Optim.Theory Appl.172, 222–235,2017. [14]R. Esp ́inola and A. Fern ́andez-Le ́on,CAT(k)-spaces, weak convergence and fixedpoints, J. Math. Anal. Appl.353, 410–427, 2009. [15]K. Goebel and S. Reich,Uniform convexity, hyperbolic geometry, and nonexpan-sive mappings. Monographs and Textbooks in Pure and Applied Mathematics, MarcelDekker Inc., New York, 1984. [16]M. Gromov and S.M. Bates,Metric structures for Riemannian and non-Riemannianspaces, Progress in Mathematics,152, eds. J. Lafontaine and P. Pansu) (Birkh ̈auser,Boston, 1999, with appendices by M. Katz, P. Pansu and S. Semmes. [17]O. G ̈uler,On the convergence of the proximal point algorithm for convex minimization,SIAM J. Control Optim.29, 403–419, 1991. [18]M.T. Heydari and S. Ranjbar,Halpern-type proximal point algorithm in completeCAT(0) metric spaces, An. St. Univ. Ovidius Constanta.24(3), 141–159, 2016. [19]J. J ̈ost,Nonpos