1] A. Barani, Subdifferentials of perturbed distance function in Riemannian manifolds, Optimization,67 (2018) 1849–
1868.
[2] A. Barani, Convexity of the solution set of a pseudoconvex inequality in Riemannian manifolds, Numer. Funct.
Anal. Opt., 39 (2018) 588–599.
[3] A. Barani and S. Hosseini, Characterization of solution sets of convex optimization problems in Riemannian mani-folds, Arch. Math., 114 (2020) 215–225.
[4] G. C. Bento and J. G. Melo, Subgradient method for convex feasibility on Riemannian manifolds, J. Optim. Theory
Appl., 152 (2012) 773–785.
[5] M. Bianchi and S. Schaible, An extension of pseudolinear functions and variational inequality problems, J. Optim.
Theory Appl., 104 (2000) 59–71.
[6] J. V. Burke and M. C. Ferris, Characterization of the solution sets of convex programs, Oper. Res. Lett., 10 (1991)
57–60.
[7] A. Cambini and L. M. Martein, Generalized Convexity and Optimization, Theory and Applications, Lecture Notes
in Economics and Mathematical Systems, 616, Springer-Verlag, Berlin Heidelberg, 2009.
[8] L. Carosi, Pseudoconvexity on a closed convex set: an application to a wide class of generalized fractional functions,
Decisions Econ. Finan., 40 (2017) 145–158.
[9] S. Chen, Existence results for vector variational inequality problems on Hadamard manifolds, Optim. Lett., 14
(2020) 2395–2411.
[10] S. Chen and C. Fang, Vector variational inequality with pseudoconvexity on Hadamard manifolds, Optimization,
65 (2016) 2067–2080.
[11] M. P. do Carmo, Riemannian Geometry, Birkhäuser, Boston, 1992.
[12] M. Farrokhiniya and A. Barani, Limiting subdifferential calculus and perturbed distance function in Riemannian
manifolds, J. Glob. Optim., 77 (2020) 661–685.
[13] O. P. Ferreira, Proximal subgradient and a characterization of Lipschitz functions on Riemannian manifolds, J.
Math. Anal. Appl., 313 (2006) 587–597.
[14] O. P. Ferreira, A. N. Iusem and S. Z. Németh, Concepts and techniques of optimization on the sphere, TOP, 22
(2014) 1148–1170.
[15] V. I. Ivanov, Characterizations of the solution sets of generalized convex minimization problems, Serdica Math. J.,
29 (2003) 1–10.
[16] V. I. Ivanov, On variational inequalities and nonlinear programming problem, Stud. Sci. Math. Hungar., 45 (2008)
483–491.
[17] V. I. Ivanov, Optimization and variational inequalities with pseudoconvex functions, J. Optim. Theory Appl., 146
(2010) 602–616.
[18] V. I. Ivanov, Optimality conditions and characterizations of the solution sets in generalized convex problems and
variational inequalities, J. Optim. Theory Appl., 158 (2013) 65–84.
[19] S. Jana and C. Nahak, An introduction to mixed hemivariational inequality problems on Hadamard manifolds,
SeMA Journal, (2021), https://doi.org/10.1007/s40324-021-00249-y.
[20] V. Jeyakumar, Infinite dimensional convex programming with applications to constrained approximation, J. Optim.
Theory Appl., 75 (1992) 469–586.
[21] E. E. Levi, Studi sui punti singolari essenziali delle funzioni analitiche di due o più variabili complesse, Ann. Mat.
Pura Appl., 17 (1910) 61–68.
[22] O. L. Mangasarian, Pseudoconvex functions, SIAM J. Control, 3 (1965) 281–290.
[23] O. L. Mangasarian, A simple characterization of solution sets of convex programs, Oper. Res. Lett., 7 (1988) 21–26.
[24] J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations of Several Variables, Academic Press,
New York ,1970.
[25] E. A. P. Quiroz, E. M. Quispe and P. R. Oliveira, Steepest descent method with a generalized Armijo search for
quasiconvex functions on Riemannian manifolds, J. Math. Anal. Appl., 341 (2008) 467–477.
[26] T. Rapscák, Smooth Nonlinear Optimization in R n , Kluwer Academic, New York, 1997.
[27] T. Sakai, Riemannian Geometry, Translations of Mathematical Monographs 149, American Mathematical Society,
Providence, RI, 1996.
[28] G. J. Tang and N. J. Huang, Korpelevich’s method for variational inequality problems on Hadamard manifolds, J.
Glob. Optim., 54 (2012) 493–509.
[29] G. J. Tang, L. Zhou and N. Huang, The proximal point algorithm for pseudomonotone variational inequalities on
Hadamard manifolds, Optim. Lett., 7 (2013) 779–790.
[30] G. J. Tang, X. Wang and H. W. Liu, A projection-type method for variational inequalities on Hadamard manifolds
and verification of solution existence, Optimization, 64 1081–1096.
[31] W. A. Thompson and D. W. Parke, Some properties of generalized concave functions, Oper. Res., 21 (1973) 305–313.
[32] H. Tuy, Sur les inégalités linéaires, Colloq. Math. 13 (1964) 107–123.
[33] C. Udriste, Convex functions and Optimization methods on Riemannian Manifolds, Mathematics and its Applica-tions 297, Kluwer Academic Publishers, 1994.
[34] Li. W. Zhou, Y. B. Xiao and N. J. Huang, New characterization geodesic convexity on Hadamard manifolds, J.
Optim. Theory Appl., 172 (2017) 824–844.
