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Research Article

Two novel two-step inertial algorithms for a class of bilevel variational inequalities

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Received 18 Nov 2023, Accepted 12 Apr 2024, Published online: 30 Apr 2024

References

  • Hartman P, Stampacchia G. On some non-linear elliptic differential-functional equations. Acta Math. 1966;115:271–310. doi: 10.1007/BF02392210
  • Hlavácek I, Haslinger J, Necas J, et al. Solution of variational inequalities in mechanics. Berlin: Springer; 1998.
  • Iiduka H. Fixed point optimization algorithm and its application to power control in CDMA data networks. Math Program. 2012;133:227–242. doi: 10.1007/s10107-010-0427-x
  • Iiduka H. Fixed point optimization algorithm and its application to network bandwidth allocation. J Comput Appl Math. 2012;236:1733–1742. doi: 10.1016/j.cam.2011.10.004
  • Iiduka H. Fixed point optimization algorithms for distributed optimization in network systems. SIAM J Optim. 2013;23:1–26. doi: 10.1137/120866877
  • Alakoya TO, Mewomo QT, Gibali A. Solving split inverse problems. Carpathian J Math. 2023;39(3):583–603.
  • Okeke CC, Jolaoso LO, Shehu Y. Inertial accelerated algorithms for solving split feasibility with multiple output sets in Hilbert spaces. Int J Nonlinear Sci Num Simul. 2021;24(2):769–790. doi: 10.1515/ijnsns-2021-0116
  • Reich S, Truong MT, Mai TNH. The split feasibility problem with multiple output sets in Hilbert spaces. Optim Lett. 2020;14:2335–2353. doi: 10.1007/s11590-020-01555-6
  • Reich S, Tuyen TM. Two new self-adaptive algorithms for solving the split feasibility problem in Hilbert space. Numer Algorithms. 2024;95:1011–1032. doi:10.1007/s11075-023-01597-8
  • Thuy NTT, Nghia NT. Some novel inertial ball-relaxed CQ algorithms for solving the split feasibility problem with multiple output sets. J Appl Anal Comput. 2023;14(3):1485–1507.
  • Thuy NTT, Tung TT. A self adaptive inertial algorithm for solving variational inequalities over the solution set of the split variational inequality problem. Optim Lett. 2023;doi: 10.1007/s11590-023-02080-y.
  • Thuy NTT, Tung TT. Two relaxed CQ methods for the split feasibility problem with multiple output sets. Bull Malays Math Sci Soc. 2024;47(2):68. doi: 10.1007/s40840-023-01647-3
  • Wang F. The split feasibility problem with multiple output sets for demicontractive mappings. J Optim Theory Appl. 2022;195(3):837–853. doi: 10.1007/s10957-022-02096-x
  • Censor Y, Elfving T. A multiprojection algorithm using Bregman projections in a product space. Numer Algorithms. 1994;8:221–239. doi: 10.1007/BF02142692
  • Censor Y, Elfving T, Kopf N, et al. The multiple-sets split feasibility problem and its application. Inverse Probl. 2005;21(6):2071–2084. doi: 10.1088/0266-5611/21/6/017
  • Censor Y, Bortfeld T, Martin B, et al. A unified approach for inversion problems in intensity-modulated radiation therapy. Phys Med Biol. 2006;51:2353–2365. doi: 10.1088/0031-9155/51/10/001
  • Byrne C. Iterative oblique projection onto convex sets and the split feasibility problem. Inverse Probl. 2002;18:441–453. doi: 10.1088/0266-5611/18/2/310
  • Byrne C. A unified treatment of some iterative algorithms in signal processing and image reconstruction. Inverse Probl. 2004;20:103–120. doi: 10.1088/0266-5611/20/1/006
  • Landweber L. An iterative formula for Fredholm integral equations of the first kind. Am J Math. 1951;73:615–624. doi: 10.2307/2372313
  • Cuong TL, Anh TV, Van THM. A self-adaptive step size algorithm for solving variational inequalities with the split feasibility problem with multiple output sets constraints. Numer Funct Anal Optim. 2022;43(9):1009–1026. doi: 10.1080/01630563.2022.2071939
  • Thuy NTT. A strong convergence theorem for an iterative method for solving the split variational inequalities in Hilbert spaces. Vietnam J Math. 2022;50(1):69–86. doi: 10.1007/s10013-021-00476-w
  • Thuy NTT, Nghia NT. A parallel algorithm for generalized multiple-set split feasibility with application to optimal control problems. Taiwan J Math. 2022;26(5):1069–1092.
  • Thuy NTT, Nghia NT. A new iterative method for solving the multipleset split variational inequality problem in Hilbert spaces. Optimization. 2023;72:1549–1575. doi: 10.1080/02331934.2022.2031193
  • Thuy NTT, Nghia NT. A hybrid projection method for solving the multiple-sets split feasibility problem. Comput Appl Math. 2023;42(6):292. doi: 10.1007/s40314-023-02416-5
  • Thuy NTT, Nghia NT. An inertial-type algorithm for a class of bilevel variational inequalities with the split variational inequality problem constraints. Optimization. 2023;doi: 10.1080/02331934.
  • Uzor V, Alakoya T, Mewomo OT. On split monotone variational inclusion problem with multiple output sets with fixed point constraints. Comput Methods Appl Math. 2023;23(3):729–749. doi: 10.1515/cmam-2022-0199
  • Yamada I. The hybrid steepest descent method for the variational inequality problem over the intersection of fixed point sets of nonexpansive mappings. Stud Comput Math. 2001;8:473–504.
  • Petrot N, Prangprakhon M, Promsinchai P, et al. A dynamic distributed conjugate gradient method for variational inequality problem over the common fixed-point constraints. Numer Algor. 2023;93:639–668. doi: 10.1007/s11075-022-01430-8
  • Polyak BT. Some methods of speeding up the convergence of iteration methods. USSR Comput Math Math Phys. 1964;4:1–17. doi: 10.1016/0041-5553(64)90137-5
  • Jia H, Liu S, Dang Y. An inertial accelerated algorithm for solving split feasibility problem with multiple output sets. Hindawi J Math. 2021;Article ID 6252984.
  • Liang J. Convergence rates of first-order operator splitting methods [Ph.D. Thesis]. Normaundie. France: Normandie Universite; 2016.
  • Iyiola OS, Shehu Y. Convergence results of two-step inertial proximal point algorithm. Appl Numer Math. 2022;182:57–75. doi: 10.1016/j.apnum.2022.07.013
  • Izuchukwu C, Shehu Y, Dong QL. Two-step inertial forward-reflected-backward splitting based algorithm for nonconvex mixed variational inequalities. J Comput Appl Math. 2023;426:115093. doi: 10.1016/j.cam.2023.115093
  • Jolaoso LO, Shehu Y, Yao JC. Strongly convergent inertial proximal point algorithm without on-line rule. J Optim Theory Appl. 2024;200:555–584. doi: 10.1007/s10957-023-02355-5
  • Bauschke HH, Combettes PL. Convex analysis and monotone operator theory in Hilbert spaces. Springer International Publishing; 2011.
  • Goebel K, Kirk WA. Topics in metric fixed point theory. Cambridge: Cambridge University Press; 1990. (Cambridge studies in advanced mathematics; 28).
  • Maingé PE. 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
  • Xu HK. Iterative algorithms for nonlinear operators. J Lond Math Soc. 2002;66(1):240–256. doi: 10.1112/jlms.2002.66.issue-1
  • Bauschke HH, Borwein JM. On projection algorithms for solving convex feasibility problems. SIAM Rev. 1996;38:367–426. doi: 10.1137/S0036144593251710

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