Convergence results on the general inertial Mann–Halpern and general inertial Mann algorithms
Tóm tắt
In this paper, we prove strong convergence theorem of the general inertial Mann–Halpern algorithm for nonexpansive mappings in the setting of Hilbert spaces. We also prove weak convergence theorem of the general inertial Mann algorithm for k-strict pseudo-contractive mappings in the setting of Hilbert spaces. These convergence results extend and generalize some existing results in the literature. Finally, we provide examples to verify our main results.
Tài liệu tham khảo
Alvarez, F.: Weak convergence of a relaxed and inertial hybrid projection-proximal point algorithm for maximal monotone operators in Hilbert space. SIAM J. Optim. 14(3), 773–782 (2004)
Alvarez, F., Attouch, H.: An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping. Set-Valued Anal. 9, 3–11 (2001)
Bauschke, H.H., Combettes, P.L.: Convex Analysis and Monotone Operator Theory in Hilbert Spaces (Vol. 408). Springer, New York (2011)
Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2(1), 183–202 (2009)
Bot, R.I., Csetnek, E.R.: A hybrid proximal-extragradient algorithm with inertial effects. Numer. Funct. Anal. Optim. 36(8), 951–963 (2015)
Bot, R.I., Csetnek, E.R., Hendrich, C.: Inertial Douglas-Rachford splitting for monotone inclusion problems. Appl. Math. Comput. 256, 472–487 (2015)
Chambolle, A., Dossal, C.: On the convergence of the iterates of the “fast iterative shrinkage/thresholding algorithm”. J. Optim. Theory Appl. 166, 968–982 (2015)
Chen, C., Chan, R.H., Ma, S., Yang, J.: Inertial proximal ADMM for linearly constrained separable convex optimization. SIAM J. Imaging Sci. 8(4), 2239–2267 (2015)
Chen, P., Huang, J., Zhang, X.: A primal-dual fixed point algorithm for convex separable minimization with applications to image restoration. Inverse Probl. 29(2), 025011 (2013)
Cholamjiak, W., Cholamjiak, P., Suantai, S.: An inertial forward-backward splitting method for solving inclusion problems in Hilbert spaces. J. Fixed Point Theory Appl. 20, 1–17 (2018)
Dong, Q.L., Cho, Y.J., Rassias, T.M.: General inertial Mann algorithms and their convergence analysis for nonexpansive mappings. Appl. Nonlinear Anal. 2018, 175–191 (2018)
Iiduka, H.: Iterative algorithm for triple-hierarchical constrained nonconvex optimization problem and its application to network bandwidth allocation. SIAM J. Optim. 22, 862–878 (2012)
Iiduka, H.: Fixed point optimization algorithms for distributed optimization in networked systems. SIAM J. Optim. 23, 1–26 (2013)
Liu, L., Qin, X.: On the strong convergence of a projection-based algorithm in Hilbert spaces. J. Appl. Anal. Comput. 10, 104–117 (2019)
Mainge, P.E.: Convergence theorems for inertial KM-type algorithms. J. Comput. Appl. Math. 219(1), 223–236 (2008)
Mann, W.R.: Mean value methods in iteration. Proc. Am. Math. Soc. 4(3), 506–510 (1953)
Micchelli, C.A., Shen, L., Xu, Y.: Proximity algorithms for image models: denoising. Inverse Probl. 27(4), 045009 (2011)
Taddele, G.H., Gebrie, A.G., Abubakar, J.: An iterative method with inertial effect for solving multiple-set split feasibility problem. Bangmod Int. J. Math. Comput. Sci. 7(2), 53–73 (2021)
Taddele, G.H., Kumam, P., Berinde, V.: An extended inertial Halpern-type ball-relaxed CQ algorithm for multiple-sets split feasibility problem. Ann. Funct. Anal. 13(3), 48 (2022)
Taddele, G.H., Kumam, P., Gebrie, A.G.: An inertial extrapolation method for multiple-set split feasibility problem. J. Inequal. Appl. 2020(1), 1 (2020)