A viscosity-type scheme for optimization problems in Hadamard spaces with applications

References

• Alakoya T, Mewomo O. S-iteration inertial subgradient extragradient method for variational inequality and fixed point problems. Optimization, 2023. p. 1–41.
   Google Scholar
• Alakoya TO, Mewomo OT. Viscosity s-iteration method with inertial technique and self-adaptive step size for split variational inclusion, equilibrium and fixed point problems. Comput Appl Math. 2022;41(1):39. doi:10.1007/s40314-021-01749-3
   Google Scholar
• Alakoya TO, Uzor VA, Mewomo OT, et al. On a system of monotone variational inclusion problems with fixed-point constraint. J Inequal Appl. 2022;2022(1):47. doi:10.1186/s13660-022-02782-4
   Web of Science ®Google Scholar
• Güler O. On the convergence of the proximal point algorithm for convex minimization. SIAM J Control Optim. 1991;29(2):403–419. doi:10.1137/0329022
   Web of Science ®Google Scholar
• Izuchukwu C, Okeke CC, Isiogugu FO. A viscosity iterative technique for split variational inclusion and fixed point problems between a hilbert space and a banach space. J Fixed Point Theory Appl. 2018;20(4):1–25. doi:10.1007/s11784-018-0632-4
   Web of Science ®Google Scholar
• Kamimura S, Takahashi W. Approximating solutions of maximal monotone operators in Hilbert spaces. J Approx Theory. 2000;106(2):226–240. doi:10.1006/jath.2000.3493
   Web of Science ®Google Scholar
• Martinet B. Brève communication. régularisation d'inéquations variationnelles par approximations successives. Rev Fr Inform Rech Oper Serie Rouge. 1970;4(R3):154–158. doi:10.1051/m2an/197004R301541
   Google Scholar
• Rockafellar RT. Monotone operators and the proximal point algorithm. SIAM J Control Optim. 1976;14(5):877–898. doi:10.1137/0314056
   Web of Science ®Google Scholar
• Takahashi W, Shimoji K. Convergence theorems for nonexpansive mappings and feasibility problems. Math Comput Model. 2000;32(11-13):1463–1471. doi:10.1016/S0895-7177(00)00218-1
   Google Scholar
• Bacak M. Old and new challenges in Hadamard spaces. arXiv preprint arXiv:1807.01355. 2018.
   Google Scholar
• Bridson MR, Haefliger A. Metric spaces of non-positive curvature. Berlin: Springer-Verlag; 1999.
   Google Scholar
• Brown KS. Buildings. In Buildings, Springer; 1989. p. 76–98.
   Google Scholar
• Dehghan H, Izuchukwu C, Mewomo O, et al. Iterative algorithm for a family of monotone inclusion problems in CAT(0) spaces. Quaest Math. 2020;43(7):975–998. doi:10.2989/16073606.2019.1593255
   Web of Science ®Google Scholar
• Kirk W, Shahzad N. Fixed point theory in distance spaces. Cham, Switzerland: Springer; 2014.
   Google Scholar
• Berg ID, Nikolaev IG. Quasilinearization and curvature of Aleksandrov spaces. Geom Dedicata. 2008;133(1):195–218. doi:10.1007/s10711-008-9243-3
   Web of Science ®Google Scholar
• Kakavandi BA, Amini M. Duality and subdifferential for convex functions on complete CAT(0) metric spaces. Nonlinear Anal Theory Methods Appl. 2010;73(10):3450–3455. doi:10.1016/j.na.2010.07.033
   Web of Science ®Google Scholar
• Khatibzadeh H, Ranjbar S. Monotone operators and the proximal point algorithm in complete CAT(0) metric spaces. J Aust Math Soc. 2017;103(1):70–90. doi:10.1017/S1446788716000446
   Web of Science ®Google Scholar
• Ranjbar S, Khatibzadeh H. Strong and Δ-convergence to a zero of a monotone operator in CAT(0) spaces. Mediterr J Math. 2017;14(2):1–15. doi:10.1007/s00009-017-0885-y
   Web of Science ®Google Scholar
• Okeke CC, Izuchukwu C. A strong convergence theorem for monotone inclusion and minimization problems in complete cat (0) spaces. Optim Methods Softw. 2019;34(6):1168–1183. doi:10.1080/10556788.2018.1472259
   Web of Science ®Google Scholar
• Chaipunya P, Kumam P. On the proximal point method in Hadamard spaces. Optimization. 2017;66(10):1647–1665. doi:10.1080/02331934.2017.1349124
   Web of Science ®Google Scholar
• Khammahawong K, Kumam P, Chaipunya P, et al. Tseng's methods for inclusion problems on Hadamard manifolds. Optimization, 2021. p. 1–35.
   Google Scholar
• Khammahawong K, Kumam P, Chaipunya P, et al. An extragradient algorithm for strongly pseudomonotone equilibrium problems on Hadamard manifolds. Thai J Math. 2020;18(1):350–371.
   Web of Science ®Google Scholar
• Salisu S, Kumam P, Sriwongsa S. One step proximal point schemes for monotone vector field inclusion problems. AIMS Math. 2022a;7(5):7385–7402. doi: 10.3934/math.2022412
   Web of Science ®Google Scholar
• Salisu S, Kumam P, Sriwongsa S. Strong convergence theorems for fixed point of multi-valued mappings in Hadamard spaces. J Inequal Appl. 2022b;2022(1):1–28. doi:10.1186/s13660-022-02870-5
   Web of Science ®Google Scholar
• Salisu S, Kumam P, Sriwongsa S. On fixed points of enriched contractions and enriched nonexpansive mappings. Carpathian J Math. 2023a;39(1):237–254. doi:10.37193/CJM
   Web of Science ®Google Scholar
• Salisu S, Kumam P, Sriwongsa S, et al. On minimization and fixed point problems in Hadamard spaces. Comput Appl Math. 2022c;41(3):117. doi:10.1007/s40314-022-01821-6
   Google Scholar
• Salisu S, Minjibir MS, Kumam P, et al. Convergence theorems for fixed points in cat p (0) spaces. J Appl Math Comput. 2023b;69(1):631–650. doi:10.1007/s12190-022-01763-6
   Web of Science ®Google Scholar
• Suparatulatorn R, Cholamjiak P, Suantai S. On solving the minimization problem and the fixed-point problem for nonexpansive mappings in cat (0) spaces. Optim Methods Softw. 2017;32(1):182–192. doi:10.1080/10556788.2016.1219908
   Web of Science ®Google Scholar
• Chaipunya P, Kohsaka F, Kumam P. Monotone vector fields and generation of nonexpansive semigroups in complete CAT(0) spaces. Numerical Functional Analysis and Optimization, 2021. p. 1–30.
   Google Scholar
• Song Y, Liu X. Convergence comparison of several iteration algorithms for the common fixed point problems. Fixed Point Theory Appl. 2009;2009:1–13. doi:10.1155/2009/824374
   Google Scholar
• Bruhat F, Tits J. Groupes réductifs sur un corps local. Publ Math Inst Hautes Etudes Sci. 1972;41(1):5–251. doi:10.1007/BF02715544
   Google Scholar
• Goebel K, Simeon R. Uniform convexity, hyperbolic geometry, and nonexpansive mappings. New York: Marcel Dekker Inc.; 1984.
   Google Scholar
• Kirk W. Fixed point theorems in spaces and-trees. Fixed Point Theory Appl. 2004;2004(4):1–8. doi:10.1155/S1687182004406081
   Google Scholar
• Reich S, Shafrir I. Nonexpansive iterations in hyperbolic spaces. Nonlinear Anal Theory Methods Appl. 1990;15(6):537–558. doi:10.1016/0362-546X(90)90058-O
   Web of Science ®Google Scholar
• Dhompongsa S, Kirk WA, Sims B. Fixed points of uniformly Lipschitzian mappings. Nonlinear Anal Theory Methods Appl. 2006;65(4):762–772. doi:10.1016/j.na.2005.09.044
   Web of Science ®Google Scholar
• Kirk W, Panyanak B. A concept of convergence in geodesic spaces. Nonlinear Anal Theory Methods Appl. 2008;68(12):3689–3696. doi:10.1016/j.na.2007.04.011
   Web of Science ®Google Scholar
• Dhompongsa S, Kirk W, Panyanak B. Nonexpansive set-valued mappings in metric and Banach spaces. J Nonlinear Convex Anal. 2007;8(1):35.
   Web of Science ®Google Scholar
• Dhompongsa S, Panyanak B. On △-convergence theorems in CAT(0) spaces. Comput Math Appl. 2008;56(10):2572–2579. doi:10.1016/j.camwa.2008.05.036
   Web of Science ®Google Scholar
• Dehghan H, Rooin J. Metric projection and convergence theorems for nonexpansive mappings in Hadamard spaces. arXiv preprint arXiv:1410.1137, 2014.
   Google Scholar
• Kakavandi B. Weak topologies in complete cat(0) metric spaces. Proc Am Math Soc. 2013;141(3):1029–1039. doi:10.1090/proc/2013-141-03
   Web of Science ®Google Scholar
• Nikolaev I. The tangent cone of an Aleksandrov space of curvature ≤k. Manuscripta Math. 1995;86(1):137–147. doi:10.1007/BF02567983
   Google Scholar
• Mayer UF. Gradient flows on nonpositively curved metric spaces and harmonic maps. Commun Anal Geom. 1998;6(2):199–253. doi:10.4310/CAG.1998.v6.n2.a1
   Web of Science ®Google Scholar
• Ambrosio L, Gigli N, Savaré G. Gradient flows: in metric spaces and in the space of probability measures. Basel: Birkhäuser Verlag; 2008.
   Google Scholar
• Jost J. Convex functionals and generalized harmonic maps into spaces of non positive curvature. Comment Math Helv. 1995;70(1):659–673. doi:10.1007/BF02566027
   Google Scholar
• Ariza-Ruiz D, Leuştean L, López-Acedo G. Firmly nonexpansive mappings in classes of geodesic spaces. Trans Am Math Soc. 2014;366(8):4299–4322. doi:10.1090/tran/2014-366-08
   Web of Science ®Google Scholar
• Xu H-K. Iterative algorithms for nonlinear operators. J Lond Math Soc. 2002;66(1):240–256. doi:10.1112/jlms.2002.66.issue-1
   Web of Science ®Google Scholar
• Maingé P-E. 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
• Sturm K-T. Nonlinear Markov operators associated with symmetric Markov kernels and energy minimizing maps between singular spaces. Calc Var Partial Differ Equ. 2001;12(4):317–357. doi:10.1007/PL00009916
   Web of Science ®Google Scholar
• Sun M, Liu J, Wang Y. Two improved conjugate gradient methods with application in compressive sensing and motion control. Mathematical Problems in Engineering, 2020.
   Google Scholar
• Yahaya MM, Kumam P, Awwal AM, et al. A new generalized quasi-newton algorithm based on structured diagonal hessian approximation for solving nonlinear least-squares problems with application to 3dof planar robot arm manipulator. IEEE Access. 2022;10:10816–10826. doi:10.1109/ACCESS.2022.3144875
   Web of Science ®Google Scholar