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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 66, 2017 - Issue 12
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Original Articles

Approximating a common zero of finite family of monotone operators in Hadamard spaces

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Pages 2233-2244 | Received 21 Nov 2016, Accepted 07 Jul 2017, Published online: 09 Aug 2017

References

  • Martinet B. Régularistion d’inéquations variationnelles par approximations successive. Rev Française Informat Recher opérationnelle. 1970;4:154–158.
  • Rockafellar T. Monotone operators and the proximal point algorithm. SIAM J Control Optim. 1976;14:79–83.
  • Li C, López G, Martín-Márquez V. Monotone vector fields and the proximal point algorithm. J London Math. Soc. 2009;679:663–683.
  • Khatibzadeh H, Ranjbar S. Monotone operators and the proximal point algorithm in complete CAT(0) metric spaces. J Aust Math Soc. 2017;103:70–90.
  • Bridson M, Haefliger A. Metric spaces of non-positive curvature. Vol. 319. Berlin: Springer; 1999.
  • Burago D, Burago Y, Ivanov S. A course in metric geometry. Vol. 33, Graduate studies in mathematics. Providence (RI): American Mathematical Society; 2001.
  • Gromov M, Bates SM. Metric structures for Riemannian and non-Riemannian spaces, with appendices by M. Katz, P. Pansu and S. Semmes, ed. by J. Lafontaine and P. Pansu. Vol. 152, Progress in mathematics. Boston: BirkhNauser; 1999.
  • Jost J. Nonpositive curvature: geometric and analytic aspects. Lectures in mathematics, ETH Zurich. Basel: Brikh\"{a}user; 1997.
  • Berg ID, Nikolaev IG. Quasilinearization and curvature of Alexandrov spaces. Geom Dedicata. 2008;133:195–218.
  • Ahmadi Kakavandi B, Amini M. Duality and subdifferential for convex functions on complete CAT(0) metric spaces. Nonlinear Anal. 2010;73:3450–3455.
  • Movahedi M, Behmardi D, Soleimani-damaneh M. On subdifferential in Hadamard spaces. Bull Iranian Math Soc. 2016;42:707–717.
  • Ahmadi Kakavandi B. Weak topologies in complete CAT(0) metric spaces. Proc Amer Math Soc. 2013;141:1029-1039.
  • Kirk WA, Panyanak B. A concept of convergence in geodesic spaces. Nonlinear Anal. 2008;68:3689–3696.
  • Ranjbar S, Khatibzadeh H. Δ-convergence and w-convegence of modiffied Mann iteration for a family of asymptotically nonexpansive type mappings in complete CAT(0) spaces. Fixed Point Theory. 2016;17:151–158.
  • Güler O. On the convergence of the proximal point algorithm for convex minimization. SIAM J Control Optim. 1991;29:403–419.
  • Brézis H, Lions P. Produits infinis de résolvantes. Israel J Math. 1978;29:329–345.
  • Djafari Rouhani B, Khatibzadeh H. On the proximal point algorithm. J Optim Theory Appl. 2008;137:411-417.
  • Bačák M. Convex analysis and optimization in Hadamard spaces. Vol. 22, De Gruyter series in nonlinear analysis and applications. Berlin: De Gruyter; 2014.
  • Verma RU. A fixed point theorem involving lipschitzian generalized pseudo-contraction. Proc Royal Irish Acad. 1997;97A:83–86.

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