Modified inertial Tseng method for solving variational inclusion and fixed point problems on Hadamard manifolds

References

• Dong Q, Jiang D, Cholamjiak P, et al. A strong convergence result involving an inertial forward–backward algorithm for monotone inclusions. J Fixed Point Theory Appl. 2017;19(4):3097–3118. doi:10.1007/s11784-017-0472-7
   Web of Science ®Google Scholar
• Gibali A, Thong DV. Tseng type methods for solving inclusion problems and its application. Calcolo. 2018;55(4):49. doi:10.1007/s10092-018-0292-1
   Web of Science ®Google Scholar
• Lions PL, Mercier B. Splitting algorithms for the sum of two nonlinear operators. SIAM J Numer Anal. 1979;16(6):964–979. doi:10.1137/0716071
   Web of Science ®Google Scholar
• Mainge F. A hybrid extragradient viscosity method for monotone operators and fixed point problems. SIAM J Control Optim. 2008;47(3):1499–1515. doi:10.1137/060675319
   Web of Science ®Google Scholar
• Tseng P. A modified forward–backward splitting method for maximal monotone mappings. SIAM J Control Optim. 2009;38(2):431–446. doi:10.1137/S0363012998338806
   Web of Science ®Google Scholar
• Combettes PL, Wajs VR. Signal recovery by proximal forward–backward splitting. Multiscale Model Simul. 2005;4(4):1168–1200. doi:10.1137/050626090
   Web of Science ®Google Scholar
• Duchi J, Singer Y. Efficient online and batch learning using forward–backward splitting. J Mach Learn Res. 2009;10:2899–2934.
   Web of Science ®Google Scholar
• Oyewole OK, Abass HA, Mebawondu AA, et al. A Tseng extragradient method for solving variational variational inequality problems in Banach spaces. Numer Algorithms. 2022;89(2):769–789. doi:10.1007/s11075-021-01133-6
   Web of Science ®Google Scholar
• Shehu Y. Convergence results of forward–backward algorithms for sum of monotone operators in Banach spaces. Results Math. 2019;74(4):138. doi:10.1007/s00025-019-1061-4
   Web of Science ®Google Scholar
• Thong DV, Cholamjiak P. Strong convergence of a forward–backward splitting method with a new step size for solving monotone inclusions. Comput Appl Math. 2019;38(2):94. doi:10.1007/s40314-019-0855-z
   Web of Science ®Google Scholar
• Sunthrayuth P, Pholasa N, Cholamjiak P. Mann-type algorithms for solving the monotone inclusion problem and fixed point problem in reflexive Banach spaces. Ric Mat. 2023;72(1):63–90. doi:10.1007/s11587-021-00596-y
   Web of Science ®Google Scholar
• Ferreira OP, Oliveira PR. Proximal point algorithm on Riemannian manifolds. Optimization. 2002;51(2):257–270. doi:10.1080/02331930290019413
   Web of Science ®Google Scholar
• Li C, López G, Màrquez VM. Resolvent of set-valued monotone vector fields in Hadamard manifolds. J Set-Valued Anal. 2011;19(3):361–383. doi:10.1007/s11228-010-0169-1
   Web of Science ®Google Scholar
• Sakai T. Riemannian geometry translations of mathematical monographs. Providence (RI): Amer. Math. Soc.; 1996.
   Google Scholar
• Baćak M. Old and new challenges in Hadamard spaces; 2018. Arxiv 1807.01355v2 Math.FA.
   Google Scholar
• Baćak M. Computing medians and means in Hadamard spaces. SIAM J Optim. 2014;24(3):1542–1566. doi: 10.1137/140953393
   Web of Science ®Google Scholar
• Baćak, The proximal point algorithm in metric spaces. Israel J Math. 2013;194:689–701. doi:10.1007/s11856-012-0091-3
   Web of Science ®Google Scholar
• Li C, López G, Martín-Márquez V. Iterative algorithms for nonexpansive mappings on Hadamard manifolds. Taiwanese J Math. 2010;14:541–559.
   Web of Science ®Google Scholar
• Ansari QH, Babu F, Ali XB. Variational inclusion problems in Hadamard manifolds. J Nonlinear Convex Anal. 2018;19(2):219–237.
   Web of Science ®Google Scholar
• Khammahawong K, Kumam P, Chaipunya P, et al. Tseng's method for inclusion problems on Hadamard manifolds. Optimization. 2022;71(15):4367–4401. doi:10.1080/02331934.2021.1940179
   Web of Science ®Google Scholar
• Polyak BT. Some methods of speeding up the convergence of iterative methods. Zh Vychisl Mat Mat Fiz. 1964;4:1–17.
   Google Scholar
• Alvarez F. On the minimizing property of a second order dissipative system in Hilbert spaces. SIAM J Control Optim. 2000;38(4):1102–1119. doi:10.1137/S0363012998335802
   Web of Science ®Google Scholar
• Antipin AS. Minimization of convex functions on convex sets by means of differential equations. Differ Eqs. 1994;30(9):1365–1375.
   Google Scholar
• Alvarez F, Attouch H. An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping. Set-Valued Anal. 2001;9(1/2):3–11. doi:10.1023/A:1011253113155
   Google Scholar
• Abass HA, Izuchukwu C, Mewomo OT, et al. Strong convergence of an inertial forward–backward splitting method for accretive operators in real Banach spaces. Fixed Point Theory. 2020;21(2):397–412. doi:10.24193/fpt-ro
   Web of Science ®Google Scholar
• Abass HA, Godwin GC, Narain OK, et al. Inertial extragradient method for solving variational inequality and fixed point problems of a Bregman demigeneralized mapping in a reflexive Banach spaces. Numer Funct Anal Optim. 2022;43(8):933–960. doi:10.1080/01630563.2022.2069813
   Web of Science ®Google Scholar
• Li X, Dong QL, Gibali A. PMICA, Parallel multi-step inertial contracting algorithm for solving common variational inclusion. J Nonlinear Funct Anal. 2022;2022:7.
   Web of Science ®Google Scholar
• Oyewole OK, Reich S. An inertial subgradient extragradient method for approximating solution to equilibrium problems in Hadamard manifold. Axioms. 2023;12(3):256. doi:10.3390/axioms12030256
   Web of Science ®Google Scholar
• Rehman HU, Kumam P, Shehu Y, et al. An inertial non-monotonic self-adaptive iterative algorithm for solving equilibrium problems. J Nonlinear Var Anal. 2022;6:51–67.
   Web of Science ®Google Scholar
• Taiwo A, Mewomo OT. Inertial viscosity with alternative regularization for certain optimization and fixed point problems. J Appl Numer Optim. 2022;4:405–423.
   Google Scholar
• Tan B, Cho SY. Strong convergence of inertial forward–backward methods for solving monotone inclusions. Appl Anal. 2022;101(15):5386–5414. doi:10.1080/00036811.2021.1892080
   Web of Science ®Google Scholar
• Khammahawong K, Chaipunya P, Kumam P. An inertial Mann algorithm for nonexpansive for nonexpansive mappings on Hadamard manifolds. AIMS Math. 2022;8(1):2093–2116. doi:10.3934/math.2023108
   Web of Science ®Google Scholar
• Onifade OM, Abass HA, Narain OK. Self-adaptive method for solving multiple set split equalityvariational inequality and fixed point problems in real Hilbert spaces. Ann Univ Ferrara. 2023. doi: 10.1007/s11565-022-00455-0
   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(3):691–708. doi:10.1007/s10957-010-9688-z
   Web of Science ®Google Scholar
• Cruz JX, Ferreira OP, Pérez LR, et al.Monotone point-to-set vector fields. Balkan J Geom Appl. 2000;5(1):69–79.
   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
• 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
• Da Cruz Neto JX, Ferreira OP, Lucambio Pérez LR, et al. Geodesic convex and monotone-transformable mathematical programming problems and a proximal-like point method. J Global Optim. 2006;35(1):53–69. doi:10.1007/s10898-005-6741-9
   Web of Science ®Google Scholar
• Udriste C. Convex functions and optimization methods on Riemannian manifolds. Dordrecht: Kluwer; 1994. (Mathematics and its applications; 297).
   Google Scholar
• Saejung S, Yotkaew P. Approximation of zeros of inverse strongly monotone operator in Banach spaces. Nonlinear Anal. 2012;75(2):742–750. doi:10.1016/j.na.2011.09.005
   Web of Science ®Google Scholar
• Liu H, Yang J. Weak convergence of iterative methods for solving quasimonotone variational inequalities. Comp Optim Appl. 2020;77(2):491–508. doi:10.1007/s10589-020-00217-8
   Web of Science ®Google Scholar
• Németh SZ. Variational inequalities on Hadamard manifolds. Nonlinear Anal. 2003;52(5):1491–1498. doi:10.1016/S0362-546X(02)00266-3
   Web of Science ®Google Scholar
• Sahu DR, Babu F, Sharma S. A new self-adaptive iterative method for variational inclusion problems on Hadamard manifolds with applications.
   Google Scholar
• Rapcsak T. Smooth nonlinear optimization in Rn. Dordrecht: Kluwer Academic Publishers; 1997.
   Google Scholar
• Sahu DR, Babu F, Sharma S. A new self-adaptive iterative method for variational inclusion problems on Hadamard manifolds with applications. Numer Algor. 2023. doi: 10.1007/s11075-023-01542-9
   Web of Science ®Google Scholar
• Sahu DR, Kumar A, Kang SM. Proximal point algorithms based on S-iterative technique for nearly asymptotically quasi-nonexpansive mappings and applications. Numer Algorithms. 2021;86(4):1561–1590. doi:10.1007/s11075-020-00945-2
   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