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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 72, 2023 - Issue 8
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Articles

An inertial Popov extragradient projection algorithm for solving multi-valued variational inequality problems

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Pages 2069-2089 | Received 25 Jul 2021, Accepted 18 Feb 2022, Published online: 25 Mar 2022

References

  • Fichera G. Problemi elastostatici con vincoli unilaterali: il problema di Signorini con ambigue condizioni al contorno. Atti Accad naz lincei Mem cl sci fis mat natur sez i. 1964;7:91–140.
  • Stampacchia G. Formes bilinéaires coercitives sur les ensembles convexes. C R Acad Sci Paris. 1964;258:4413–4416.
  • Hartman P, Stampacchia G. On some non-linear elliptic diferential–functional equations. Acta Math. 1966;115:271–310.
  • Kinderlehrer D, Stampacchia G. An introduction to variational inequalities and their applications. Philadelphia: Society for Industrial and Applied Mathematics; 2000.
  • Bertsekas DP, Tsitsiklis JN. Parallel and distributed computation: numerical methods. Englewood Cliffs, NJ: Prentice-Hall; 1989.
  • Korpelevich GM. An extragradient method for finding saddle points and for other problems. Matecon. 1976;12:747–756.
  • Censor Y, Gibali A, Reich S. The subgradient extragradient method for solving variational inequalities in Hilbert space. J Optim Theory Appl. 2011;148:318–335.
  • Fang C, He Y. A double projection algorithm for multi-valued variational inequalities and a unified framework of the method. Appl Math Comput. 2011;217:9543–9551.
  • Solodov MV, Svaiter BF. A new projection method for variational inequality problems. SIAM J Control Optim. 1999;37:765–776.
  • Xiu N, Wang Y, Zhang X. Modified fixed-point equations and related iterative methods for variational inequalities. Comput Math Appl. 2004;47:913–920.
  • Censor Y, Gibali A, Reich S. Extensions of Korpelevich's extragradient method for the variational inequality problem in Euclidean space. Optimization. 2012;61:1119–1132.
  • Browder FE. Multi-valued monotone nonlinear mappings and duality mappings in Banach spaces. Trans Am Math Soc. 1965;118:338–351.
  • Konnov IV. A combined relaxation method for variational inequalities with nonlinear constraints. Math Program. 1998;80:239–252.
  • Li F, He Y. An algorithm for generalized variational inequality with pseudomonotone mapping. J Comput Appl Math. 2009;228:212–218.
  • Ye ML. A cutting hyperplane projection method for solving generalized quasi-variational inequalities. J Oper Res Soc China. 2016;4:483–501.
  • Fang C, Chen S. A subgradient extragradient algorithm for solving multi-valued variational inequality. Appl Math Comput. 2014;229:123–130.
  • Ye ML. An improved projection method for solving generalized variational inequality problems. Optimization. 2018;67:1523–1533.
  • Dong QL, Lu YY, Yang J, et al. Approximately solving multi-valued variational inequalities by using a projection and contraction algorithm. Numer Algorithms. 2017;76:799–812.
  • Denisov SV, Semenov VV, Chabak LM. Convergence of the modifed extragradient method for variational inequalities with non-Lipschitz operators. Cybern Syst Anal. 2015;51:757–765.
  • Gibali A. A new Bregman projection method for solving variational inequalities in Hilbert spaces. Pure Appl Funct Anal. 2018;3:403–415.
  • VanHieu D, Thong DV. New extragradient-like algorithms for strongly pseudomonotone variational inequalities. J Glob Optim. 2018;70:385–399.
  • Kraikaew R, Saejung S. Strong convergence of the Halpern subgradient extragradient method for solving variational inequalities in Hilbert spaces. J Optim Theory Appl. 2014;163:399–412.
  • Ceng LC, Petrusel A, Qin X, et al. A modified inertial subgradient extragradient method for solving pseudomonotone variational inequalities and common fixed point problems. Fixed Point Theory. 2020;21:93–108.
  • Ceng L-C, Petrusel A, Yao J-C, et al. Hybrid viscosity extragradient method for systems of variational inequalities, fixed points of nonexpansive mappings, zero points of accretive operators in Banach spaces. Fixed Point Theory. 2018;19:487–502.
  • Ceng LC, Petrusel A, Qin X, et al. Pseudomonotone variational inequalities and fixed points. Fixed Point Theory. 2021;22:543–558.
  • Ceng LC, Yuan Q. Composite inertial subgradient extragradient methods for variational inequalities and fixed point problems. J Inequal Appl. 2019;1:274–294.
  • Ceng LC, Petrusel A, Qin X, et al. Two inertial subgradient extragradient algorithms for variational inequalities with fixed-point constraints. Optimization. 2021;70:1337–1358.
  • Ceng LC, Petrusel A, Wen CF, et al. Inertial-like subgradient extragradient methods for variational inequalities and fixed points of asymptotically nonexpansive and strictly pseudocontractive mappings. Mathematics. 2019;7:890–909.
  • Ceng LC, Shang M. Hybrid inertial subgradient extragradient methods for variational inequalities and fixed point problems involving asymptotically nonexpansive mappings. Optimization. 2021;70:715–740.
  • Polyak BT. Some methods of speeding up the convergence of iteration methods. USSR Comput Math Math Phys. 1964;4:1–17.
  • Dong QL, Cho YJ, Zhong LL, et al. Inertial projection and contraction algorithms for variational inequalities. J Glob Optim. 2018;70:687–704.
  • Thong DV, Vinh NT, Cho YJ. New strong convergence theorem of the inertial projection and contraction method for variational inequality problems. Numer Algorithms. 2020;84:285–305.
  • Gibali A, Hieu DV. A new inertial double-projection method for solving variational inequalities. J Fixed Point Theory Appl. 2019;21:1–21.
  • Thong DV, Li XH, Dong QL, et al. An inertial Popov's method for solving pseudomonotone variational inequalities. Optim Lett. 2021;15:757–777.
  • Facchinei F, Pang JS. Finite-dimensional variational inequalities and complementarity problems. New York: Springer-Verlag; 2003.
  • Boyd S, Vandenberghe L. Convex optimization. New York: Cambridge University Press; 2004.
  • Zarantonello EH. Projections on convex sets in Hilbert space and spectral theory: part I. Projections on convex sets: part II. Spectral theory. New York: Academic Press; 1971. p. 237–424.
  • Bauschke HH, Combettes PL. Convex analysis and monotone operator theory in Hilbert spaces. New York: Springer; 2011.
  • Malitsky YV, Semenov VV. An extragradient algorithm for monotone variational inequalities. Cybern Syst Anal. 2014;50:271–277.
  • Aubin JP, Ekeland I. Applied nonlinear analysis. New York: Courier Corporation; 2006.
  • Huebner E, Tichatschke R. Relaxed proximal point algorithms for variational inequalities with multi-valued operators. Optim Methods Softw. 2008;23:847–877.

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