[1] Absil, P. A., Mahony, R., Sepulchre, R., Optimization Algorithms on Matrix Manifolds,
Princeton University Press, Princeton, NJ, 2008.
[2] Ahmadi Kakavandi, B., Amini, M., Duality and subdifferential for convex functions on
complete CAT(0) metric spaces, Nonlinear Anal., 73 (2010), 3450–3455.
[3] Ahmadi Kakavandi, B., Weak topologies in complete CAT(0) metric spaces, Proc. Amer.
Math. Soc., 141 (2013), 1029–1039.
[4] Alexander, S., Kapovitch, V., Petrunin, A., An Invitation to Alexandrov Geometry: CAT(0)
spaces, Springer, Cham, 2019.
[5] Bačák, M., Convex Analysis and Optimization in Hadamard Spaces, De Gruyter, Berlin,
2014.
[6] de A. Bortoloti, M. A., Fernandes, T. A., Ferreira, O. P. Yuan, J., Damped Newton’s
method on Riemannian manifolds, J. Global Optim., 77 (2020), 643–660.
[7] Boyd, S., Vandenberghe, L. , Convex Optimization, Cambridge University Press, Cambridge,
2004.
[8] Bridson, M., Haefliger, A., Metric Spaces of Nonpositive Curvature, Springer, Berlin,
1999.
[9] Burago, D., Burago, Y., Ivanov, S., A Course in Metric Geometry, Amer. Math. Soc.,
Providence, RI, 2001.
[10] Gromov, M., Metric Structures for Riemannian and Non-Riemannian Spaces; reprint of
the 2001 English ed., Birkhäuser Boston, Boston, 2007.
[11] Huang, W., Absil, P. A., Gallivan, K. A., A Riemannian BFGS method for nonconvex optimization
problems, In: Numerical Mathematics and Advanced Applications (ENUMATH
2015), Lecture Notes in Computational Science and Engineering, vol. 112, Springer, Cham,
2016, 627–634.
[12] Fernandes, T. A., Ferreira, O. P., Yuan, J., On the superlinear convergence of Newton’s
method on Riemannian manifolds, J. Optim. Theory Appl., 173 (2017), 828–843.
[13] Ji, H., Optimization approaches on smooth manifolds, Ph.D. thesis, Australian National
University, Canberra, 2007.
[14] Jiang, D., Moore, J. B., Ji, H., Self-concordant functions for optimization on smooth manifolds,
J. Global Optim., 38 (2007), 437–457.
[15] Kirk, W. A., Shahzad, N., Fixed Point Theory in Distance Spaces, Springer, Cham, 2014.

[16] Lott, J., Villani, C., Ricci curvature for metric-measure spaces via optimal transport, Ann.
of Math., 169 (2009), 903–991.
[17] Manton, J. H., A framework for generalising the Newton method and other iterative methods
from Euclidean space to manifolds, Numer. Math., 129 (2015), 91–125.
[18] Nesterov, Y., Nemirovskii, A., Interior-Point Polynomial Algorithms in Convex Programming,
SIAM, Philadelphia, PA, 1994.
[19] Nesterov, Y., Todd, M., On the Riemannian geometry defined by self-concordant barriers
and interior-point methods, Found. Comput. Math., 2 (2002), 333–361.
[20] Papadopoulos, A., Metric Spaces, Convexity and Nonpositive Curvature, European Mathematical
Society, Zürich, 2005.
[21] Perelman, G., Spaces with curvature bounded below, In Proceedings of the International
Congress of Mathematicians (Zürich, 1994), Vol. 1, 2, Birkhäuser, Basel, 1995, 517–525.
[22] Smith, S., Optimization techniques on Riemannian manifolds, Fields Inst. Commun., 3
(1994), 113–146.
[23] Sormani, C., Friedmann cosmology and almost isotropy, Geom. Funct. Anal., 14 (2004),
853–912.
[24] Shalev-Shwartz, S., Ben-David, S., Understanding Machine Learning: From Theory to
Algorithms, Cambridge University Press, New York, 2014.
[25] Udrişte, C., Convex Functions and Optimization Methods on Riemannian Manifolds,
Kluwer Academic Publishers Group, Dordrecht, 1994.