과제정보
This research is funded by King Mongkuts University of Technology North Bangkok (Contract no. KMUTNB-63-KNOW-016). The last author acknowledges with thanks, the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University.
참고문헌
- F. Alvarez, On the minimizing property of a second order dissipative system in hilbert spaces, SIAM J. Control Opti., 38(4) (2000), 1102-1119. https://doi.org/10.1137/S0363012998335802
- F. Alvarez and H. Attouch, An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping, Set-Valued Anal., 9(1-2) (2001), 3-11. https://doi.org/10.1023/A:1011253113155
- K. Afassinou, O.K. Narain and O.E. Otunuga, Iterative algorithm for approximating solutions of Split Monotone Variational Inclusion, Variational inequality and fixed point problems in real Hilbert spaces, Nonlinear Func. Anal. Appl., 25(3) (2020), 491-510. https://doi.org/10.22771/NFAA.2020.25.03.06
- A. Beck and M. Teboulle, A fast iterative shrinkage-thresholding algorithm for linear inverse problems, SIAM J. Imaging Sci., 2(1) (2009), 183-202. https://doi.org/10.1137/080716542
- R.I. Bot and E.R. Csetnek, An inertial alternating direction method of multipliers, arXiv:1404.4582v1[math.OC], 2014.
- F.E. Browder, 'Fixed-point theorems for noncompact mappings in Hilbert space, Proc. Nat. Acad. Sci. USA, 53 (1965), 1272-1276. https://doi.org/10.1073/pnas.53.6.1272
- C. Chen, R.H. Chan, S. Ma and J. Yang, Inertial proximal admm for linearly constrained separable convex optimization, SIAM J. Imaging Sci., 8(4) (2015), 2239-2267. https://doi.org/10.1137/15100463X
- G.H.G. Chen and R.T. Rockafellar, Convergence rates in forward-backward splitting, SIAM J. Optim., 7(2) (1997), 421-444. https://doi.org/10.1137/S1052623495290179
- C. Chidume, Geometric Properties of Banach Spaces and Nonlinear iterations, Springer, 2009.
- C.E. Chidume, A. Adamu and M. Nnakwe, 'Strong convergence of an inertial algorithm for maximal monotone inclusions with applications, Fixed Point Theory Appl., 2020(1) (2020), 1-22. https://doi.org/10.1186/s13663-020-0669-0
- C.E. Chidume, A. Adamu and L.C. Okereke, Iterative algorithms for solutions of Hammerstein equations in real Banach spaces, Fixed Point Theory Appl., 2020(1) (2020), 1-23. https://doi.org/10.1186/s13663-020-0669-0
- C.E. Chidume, A. Adamu, M. Minjibir and U. Nnyaba, On the strong convergence of the proximal point algorithm with an application to Hammerstein euations, J. Fixed Point Theory Appl., 22(3) (2020), 1-21. https://doi.org/10.1007/s11784-019-0746-3
- C.E. Chidume, A. Adamu and L. Okereke, Approximation of solutions of hammerstein equations with monotone mappings in real Banach spaces, Carpa. J. Math., 35(3) (2019), 305-316. https://doi.org/10.37193/CJM.2019.03.05
- C.E. Chidume, A. Adamu and L.C. Okereke, A krasnoselskii-type algorithm for approximating solutions of variational inequality problems and convex feasibility problems, J. Nonlinear Var. Anal., 2(2) (2018), 203-218. https://doi.org/10.23952/jnva.2.2018.2.07
- C.E. Chidume, L. Chinwendu and A. Adamu, A hybrid algorithm for approximating solutions of a variational inequality problem and a convex feasibility problem, Adv. Nonlinear Var. Ineq., 21(1) (2018), 46-64.
- C. Chidume, S. Ikechukwu and A. Adamu, Inertial algorithm for approximating a common fixed point for a countable family of relatively nonexpansive maps, Fixed Point Theory Appl., 2018(1) (2018), 1-9. https://doi.org/10.1186/s13663-017-0625-9
- C.E. Chidume, P. Kumam and A. Adamu, A hybrid inertial algorithm for approximating solution of convex feasibility problems with applications, Fixed Point Theory and Appl., 2020(1) (2020), 1-17. https://doi.org/10.1186/s13663-020-0669-0
- C.E. Chidume and M.O. Nnakwe, Iterative algorithms for split variational inequalities and generalized split feasibility problems with applications, Nonlinear Var. Anal., 3 (2019), 127-140.
- P. Cholamjiak and Y. Shehu, Inertial forward-backward splitting method in banach spaces with application to compressed sensing, Appl. Math., 64 (2019), 409-435. https://doi.org/10.21136/AM.2019.0323-18
- P. Cholamjiak, K. Kankam, P. Srinet and N. Pholasa, A double forward-backward algorithm using line searches for minimization problem, Thai J. Math., 18(1) (2020), 63-76.
- P.L. Combettes and V.R. Wajs, Signal recovery by proximal forward-backward splitting, Multiscale Mode. Simu., 4(4) (2005), 1168-1200. https://doi.org/10.1137/050626090
- J. Dunn, Convexity, monotonicity, and gradient processes in Hilbert space, J. Math. Anal. Appl., 53(1) (1976), 145-158. https://doi.org/10.1016/0022-247X(76)90152-9
- D. Gabay, Chapter ix applications of the method of multipliers to variational inequalities in Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary-Value Problems (M. Fortin and R. Glowinski, eds.), Studies in Math. Its Appl. Elsevier, 15 (1983), 299-331.
- S. He and C. Yang, Solving the variational inequality problem defined on intersection of finite level sets, Abstr. Appl. Anal., 2013 (2013), 1-8.
- J.K. Kim and T.M. Tuyen,, New iterative methods for finding a common zero of a finitely of accretive operators in Banach spaces, J. Nonlinear Convex Anal., 21(1) (2020), 139-155.
- D. Kitkuan, P. Kumam, J. Martinez-Moreno and K. Sitthithakerngkiet, Inertial viscosity forward-backward splitting algorithm for monotone inclusions and its application to image restoration problems, Int. J. Comput. Math., 97(1-2) (2020), 482-497. https://doi.org/10.1080/00207160.2019.1649661
- D. Kitkuan, P. Kumam, A. Padcharoen, W. Kumam and P. Thounthong, Algorithms for zeros of two accretive operators for solving convex minimization problems and its application to image restoration problems, J. Comput. Appl. Math., 354 (2019), 471-495. https://doi.org/10.1016/j.cam.2018.04.057
- D. Kitkuan, P. Kumam and J. Martinez-Moreno, Generalized Halpern-type forward-backward splitting methods for convex minimization problems with application to image restoration problems, Optimization, 69(7-8) (2020), 1-25. https://doi.org/10.1080/02331934.2020.1683315
- P. Kumam and K. Wattanawitoon, Convergence theorems of a hybrid algorithm for equilibrium problems, Nonlinear Anal.: Hybrid Syst., 3(4) (2009), 386-394. https://doi.org/10.1016/j.nahs.2009.02.006
- P.L. Lions and B. Mercier, Splitting algorithms for the sum of two nonlinear operators, SIAM J. Nume. Anal., 16(6) (1979), 964-979. https://doi.org/10.1137/0716071
- D.A. Lorenz and T. Pock, An inertial forward-backward algorithm for monotone inclusions, J. Math. Imag. Vision, 51(2) (2015), 311-325. https://doi.org/10.1007/s10851-014-0523-2
- G. Lopez, V. Martin-Marquez, F.-H. Wang and H.-K. Xu, Forward-backward splitting methods for accretive operators in Banach spaces, Abstr. Appl. Anal., (2012) Article ID 109236, https://doi.org/10.1155/2012/109236
- B. Mercier, Inequations variationnelles de la mecanique. Publications mathematiques d'Orsay, Universite de Paris-Sud, Departement de mathematique, 1980.
- A. Padcharoen, P. Kumam, P. Chaipunya and Y. Shehu, Convergence of inertial modified Krasnoselskii-Mann iteration with application to image recovery, Thai J. Math., 18(1) (2020), 126-141.
- G.B. Passty, Ergodic convergence to a zero of the sum of monotone operators in Hilbert space, J. Math. Anal. Appl., 72(2) (1979), 383-390. https://doi.org/10.1016/0022-247x(79)90234-8
- B.T. Polyak, Some methods of speeding up the convergence of iteration methods, USSR Comput. Math. Math. Phys., 4(5) (1964), 1-17. https://doi.org/10.1016/0041-5553(64)90137-5
- S. Reich, Strong convergence theorems for resolvents of accretive operators in banach spaces, J. Math. Anal. Appl., 75(1) (1980), 287-292. https://doi.org/10.1016/0022-247x(80)90323-6
- R. Rockafellar, On the maximality of sums of nonlinear monotone operators, Trans. Amer. Math. Soc., 149(1) (1970), 75-88. https://doi.org/10.1090/S0002-9947-1970-0282272-5
- S. Saewan, P. Kumam and Y.J. Cho, Convergence theorems for finding zero points of maximal monotone operators and equilibrium problems in Banach spaces, J. Inequal. Appl., 2013 (2013), 1-18. https://doi.org/10.1186/1029-242X-2013-1
- S. Saewan, P. Kumam and Y.J. Cho, Strong convergence for maximal monotone operators, relatively quasi-nonexpansive mappings, variational inequalities and equilibrium problems, J. Global Optim., 57 (2013), 1299-1318. https://doi.org/10.1007/s10898-012-0030-1
- S. Saewan and P. Kumam, A modified hybrid projection method for solving generalized mixed equilibrium problems and fixed point problems in Banach spaces, Comput. Math. Appl., 62(4) (2011), 1723-1735. https://doi.org/10.1016/j.camwa.2011.06.014
- P. Sunthrayuth and P. Cholamjiak, A modified extragradient method for variational inclusion and fixed point problems in banach spaces, Applicable Anal., (2019), 1-20, https://doi.org/10.1080/00036811.2019.1673374.
- W. Takahashi, N.-C. Wong, J.-C. Yao, Two generalized strong convergence theorems of Halpern's type in Hilbert spaces and applications, Taiwanese J. Math., 16(3) (2012), 1151-1172. https://doi.org/10.11650/twjm/1500406684
- S. Takahashi, W. Takahashi and M. Toyoda, Strong convergence theorems for maximal monotone operators with nonlinear mappings in Hilbert spaces, J. Opti. Theory Appl., 147 (2010), 27-41. https://doi.org/10.1007/s10957-010-9713-2
- D.V. Thong and P. Cholamjiak, Strong convergence of a forward-backward splitting method with a new step size for solving monotone inclusions, Comput. Appl. Math., 38:94 (2019). https://doi.org/10.1007/s40314-019-0855-z
- P. Tseng, A modified forward-backward splitting method for maximal monotone mappings, SIAM J. Control Opti., 38(2) (2000), 431-446. https://doi.org/10.1137/S0363012998338806
- T.M. Tuyen, On the strong convergence theorem of the hybrid viscosity approximation method for zero of m-accretive operators in Banach spaces, Nonlinear Func. Anal. Appl., 22(2) (2017), 287-299.
- A.Y. Wang and Z.M. Wang, A simple hybrid Bregman projection algorithms for a family of countable Bregman quasi-strict pseudo-contractions, Nonlinear Func. Anal. Appl., 22(5) (2017), 1001-1011. https://doi.org/10.22771/NFAA.2017.22.05.05
- H. Zegeye and N. Shahzad, Strong convergence theorems for a common zero for a finite family of m-accretive mappings, Nonlinear Anal., 66 (2007), 1161-1169. https://doi.org/10.1016/j.na.2006.01.012