Iterative approximation of common solution to variational inequality problems in Hadamard manifold

References

• Fichera G. Sul problema elastostatico di Signorini con ambigue condizioni al contorno. Atti Accad Naz Lincei VIII Ser Rend Cl Sci Fis Mat Nat. 1963;34:138–142.
   Google Scholar
• Stampacchia G. Formes bilineaires coercitives sur les ensembles convexes. C R Acad Sci. 1964;258:4413–4416. Paris.
   Google Scholar
• Kinderlehrer D, Stampacchia G. An introduction to variational inequalities and their applications. New York-London: Academic Press; 1980.
   Google Scholar
• Censor Y, Gibali A, Reich S. The subgradient extragradient method for solving variational inequalities in Hilbert space. J Optim Theory Appl. 2011;148:318–335. doi: 10.1007/s10957-010-9757-3
   PubMed Web of Science ®Google Scholar
• Hieu DV. Parallel and cyclic hybrid subgradient extragradient methods for variational inequalities. Afr Mat. 2017;28:677–692. doi: 10.1007/s13370-016-0473-5
   Web of Science ®Google Scholar
• Korpelevich GM. The extragradient method for finding saddle points and other problems. Ekon Mat Metody. 1976;12:747–756.
   Google Scholar
• Oyewole OK, Abass HA, Mebawondu AA, et al. A Tseng extragradient method for solving variational inequality problems in Banach spaces. Numer Alg; 2021:1–21.
   Google Scholar
• Dafermos S. Traffic equilibrium and variational inequalities. Trans Sci. 1980;14:42–54. doi: 10.1287/trsc.14.1.42
   Web of Science ®Google Scholar
• Tseng P. A modified forward-backward splitting method for maximal monotone mappings. SIAM J Control Optim. 2000;38:431–446. doi: 10.1137/S0363012998338806
   Web of Science ®Google Scholar
• Rehman H, Kumam P, Dong QL, et al. A modified self-adaptive extragradient method for pseudomonotone equilibrium problem in a real Hilbert space with applications. Math Met Appl Sci. 2021;44:3527–3547. doi: 10.1002/mma.v44.5
   Web of Science ®Google Scholar
• Thong DV, Hieu DV, Rassias TM. Self adaptive inertial subgradient extragradient algorithms for solving pseudomonotone variational inequality problems. Optim Lett. 2020;14:115–144. doi: 10.1007/s11590-019-01511-z
   Web of Science ®Google Scholar
• Bauschke HH, Borwein JM. On projection algorithms for solving convex feasibility problems. SIAM Rev. 1996;38:367–426. doi: 10.1137/S0036144593251710
   Web of Science ®Google Scholar
• Stark H. Image recovery theory and applications. Orlando: Academic; 1987.
   Google Scholar
• Censor Y, Gibali A, Reich S, et al. Common solutions to variational inequalities. Set Val Var Anal. 2012;20:229–247. doi: 10.1007/s11228-011-0192-x
   Web of Science ®Google Scholar
• Khammahawong K, Kumam P, Chaipunya P, et al. New Tseng's extragradient methods for pseudomonotone variational inequality problems in Hadamard manifolds. Fixed Point Theory Alg Sci Eng. 2021;2021:1–20. doi: 10.1186/s13663-021-00689-1
   Google Scholar
• Tang G, Wang X, Liu HW. A projection-type method for variational inequalities on Hadamard manifolds and verification of solution existence. Optimization. 2015;64(5):1081–1096. doi: 10.1080/02331934.2013.840622
   Web of Science ®Google Scholar
• Tang G, Huang N. Korpelevich's method for variational inequality problems on Hadamard manifolds. J Glob Optim. 2012;54(3):493–509. doi: 10.1007/s10898-011-9773-3
   Web of Science ®Google Scholar
• Chen J, Liu S, Chang X. Modified Tseng's extragradient methods for variational inequality on Hadamard manifolds. Appl Anal. 2021;100(12):2627–2640. doi: 10.1080/00036811.2019.1695783
   Web of Science ®Google Scholar
• He H, Peng J, Li H. Iterative approximation of fixed point problems and variational inequality problems on Hadamard manifolds. UPB Sci Bull Ser A. 2022;84(1):25–36.
   Google Scholar
• Polyak BT. Some methods of speeding up the convergence of iteration methods. USSR Comput Math Math Phys. 1964;4(5):1–17. doi: 10.1016/0041-5553(64)90137-5
   Google Scholar
• Nesterov Y. A method for solving the convex programming problem with convergence rate O(1k2). Dokl Akad Nauk SSSR. 1983;269(3):543–547.
   Google Scholar
• Sakai T. Riemannian geometry. Vol. 149, Translations of mathematical monographs, Providence (RI): American Mathematical Society; 1996. Translated from the 1992 Japanese original by the author.
   Google Scholar
• Wang JH, López G, Martín-Márquez V, et al. Monotone and accretive vector fields on Riemannian manifolds. J Optim Theory Appl. 2010;146:691–708. doi: 10.1007/s10957-010-9688-z
   Web of Science ®Google Scholar
• Bridson MR, Haefliger A. Metric spaces of non-positive curvature. Berlin : Springer; 1999. (Grundlehren der Mathematischen Wissenschaften (Fundamental Principles of Mathematical Sciences); Vol. 319). doi: 10.1007/978-3-662-12494-9
   Google Scholar
• Li C, López G, Martín-Márquez V. Monotone vector fields and the proximal point algorithm on Hadamard manifolds. J Lond Math Soc. 2009;79(3):663–683. doi: 10.1112/jlms/jdn087
   Web of Science ®Google Scholar
• Takahashi W. Introduction to nonlinear and convex analysis. Yokohama: Yokohama Publishers; 2009.
   Google Scholar
• Xu HK. An iterative approach to quadratic optimization. J Optim Theory Appl. 2003;116:659-678. doi: 10.1023/A:1023073621589
   Web of Science ®Google Scholar
• Maingé PE. Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization. Set-Valued Anal. 2008;16(7-8):899–912. doi: 10.1007/s11228-008-0102-z
   Google Scholar