Modified inertial projection and contraction algorithms with non-monotonic step sizes for solving variational inequalities and their applications

References

• Vuong PT, Shehu Y. Convergence of an extragradient-type method for variational inequality with applications to optimal control problems. Numer Algorithms. 2019;81(1):269–291.
   Web of Science ®Google Scholar
• Chen J, Köbis E, Yao JC. Optimality conditions and duality for robust nonsmooth multiobjective optimization problems with constraints. J Optim Theory Appl. 2019;181(2):411–436.
   Web of Science ®Google Scholar
• Chen J, Ju X, Köbis E, et al. Tikhonov type regularization methods for inverse mixed variational inequalities. Optimization. 2020;69(2):401–413.
   Web of Science ®Google Scholar
• Ansari QH, Islam M, Yao JC. Nonsmooth variational inequalities on Hadamard manifolds. Appl Anal. 2020;99(2):340–358.
   Web of Science ®Google Scholar
• Zhao X, Köbis MA, Yao Y, et al. A projected subgradient method for nondifferentiable quasiconvex multiobjective optimization problems. J Optim Theory Appl. 2021;190(1):82–107.
   Web of Science ®Google Scholar
• Korpelevich GM. The extragradient method for finding saddle points and other problems. Èkonom i Mat Metody. 1976;12(4):747–756.
   Google Scholar
• Tseng P. A modified forward-backward splitting method for maximal monotone mappings. SIAM J Control Optim. 2000;38(2):431–446.
   Web of Science ®Google Scholar
• He BS. A class of projection and contraction methods for monotone variational inequalities. Appl Math Optim. 1997;35(1):69–76.
   Web of Science ®Google Scholar
• Censor Y, Gibali A, Reich S. The subgradient extragradient method for solving variational inequalities in Hilbert space. J Optim Theory Appl. 2011;148(2):318–335.
   PubMed Web of Science ®Google Scholar
• Censor Y, Gibali A, Reich S. Extensions of Korpelevich's extragradient method for the variational inequality problem in Euclidean space. Optimization. 2012;61(9):1119–1132.
   Web of Science ®Google Scholar
• Censor Y, Gibali A, Reich S. Strong convergence of subgradient extragradient methods for the variational inequality problem in Hilbert space. Optim Methods Softw. 2011;26(4–5):827–845.
   Web of Science ®Google Scholar
• Malitsky Y. Projected reflected gradient methods for variational inequalities. SIAM J Optim. 2015;25(1):502–520.
   Web of Science ®Google Scholar
• Dong QL, Jiang D, Gibali A. A modified subgradient extragradient method for solving the variational inequality problem. Numer Algorithms. 2018;79(3):927–940.
   Web of Science ®Google Scholar
• Bauschke HH, Combettes PL. A weak-to-strong convergence principle for Fejér-monotone methods in Hilbert spaces. Math Oper Res. 2001;26(2):248–264.
   Web of Science ®Google Scholar
• Shehu Y, Dong QL, Jiang D. Single projection method for pseudo-monotone variational inequality in Hilbert spaces. Optimization. 2019;68(1):385–409.
   Web of Science ®Google Scholar
• Gibali A, Thong DV, Tuan PA. Two simple projection-type methods for solving variational inequalities. Anal Math Phys. 2019;9(4):2203–2225.
   Web of Science ®Google Scholar
• Thong DV, Gibali A. Two strong convergence subgradient extragradient methods for solving variational inequalities in Hilbert spaces. Jpn J Ind Appl Math. 2019;36(1):299–321.
   Web of Science ®Google Scholar
• Cholamjiak P, Thong DV, Cho YJ. A novel inertial projection and contraction method for solving pseudomonotone variational inequality problems. Acta Appl Math. 2020;169(1):217–245.
   Web of Science ®Google Scholar
• Jolaoso LO. An inertial projection and contraction method with a line search technique for variational inequality and fixed point problems. Optimizaiton. 2021. DOI:10.1080/02331934.2021.1901289.
   PubMed Web of Science ®Google Scholar
• Beck A, Teboulle M. A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J Imaging Sci. 2009;2(1):183–202.
   Web of Science ®Google Scholar
• Chambolle A, Dossal C. On the convergence of the iterates of the “Fast Iterative Shrinkage/Thresholding Algorithm”. J Optim Theory Appl. 2015;166(3):968–982.
   Web of Science ®Google Scholar
• Attouch H, Cabot A. Convergence rates of inertial forward-backward algorithms. SIAM J Optim. 2018;28(1):849–874.
   Web of Science ®Google Scholar
• Dong QL, Cho YJ, Zhong LL, et al. Inertial projection and contraction algorithms for variational inequalities. J Global Optim. 2018;70(3):687–704.
   Web of Science ®Google Scholar
• Hieu DV, Strodiot JJ, Muu LD. An explicit extragradient algorithm for solving variational inequalities. J Optim Theory Appl. 2020;185(2):476–503.
   Web of Science ®Google Scholar
• Shehu Y, Iyiola OS. Projection methods with alternating inertial steps for variational inequalities: weak and linear convergence. Appl Numer Math. 2020;157:315–337.
   Web of Science ®Google Scholar
• Shehu Y, Gibali A. New inertial relaxed method for solving split feasibilities. Optim Lett. 2021;15(6):2109–2126.
   Web of Science ®Google Scholar
• Gibali A, Jolaoso LO, Mewomo OT, et al. Fast and simple Bregman projection methods for solving variational inequalities and related problems in Banach spaces. Results Math. 2020;75(4):179.
   Web of Science ®Google Scholar
• Jolaoso LO, Alakoya TO, Taiwo A, et al. Inertial extragradient method via viscosity approximation approach for solving equilibrium problem in Hilbert space. Optimization. 2021;70(2):387–412.
   Web of Science ®Google Scholar
• Tan B, Li S, Cho SY. Inertial projection and contraction methods for pseudomonotone variational inequalities with non-Lipschitz operators and applications. Appl Anal. 2021. DOI:10.1080/00036811.2021.1979219.
   Web of Science ®Google Scholar
• Yang J, Liu H. Strong convergence result for solving monotone variational inequalities in Hilbert space. Numer Algorithms. 2019;80(3):741–752.
   Web of Science ®Google Scholar
• Liu H, Yang J. Weak convergence of iterative methods for solving quasimonotone variational inequalities. Comput Optim Appl. 2020;77(2):491–508.
   Web of Science ®Google Scholar
• Hieu DV, Anh PK, Muu LD. Modified extragradient-like algorithms with new stepsizes for variational inequalities. Comput Optim Appl. 2019;73(3):913–932.
   Web of Science ®Google Scholar
• Jolaoso LO, Shehu Y. Single Bregman projection method for solving variational inequalities in reflexive Banach spaces. Appl Anal. 2022;101(14):4807–4828. DOI:10.1080/00036811.2020.1869947.
   Web of Science ®Google Scholar
• Thong DV, Long LV, Li XH, et al. A new self-adaptive algorithm for solving pseudomonotone variational inequality problems in Hilbert spaces. Optimization. 2021. DOI:10.1080/02331934.2021.1909584.
   PubMed Web of Science ®Google Scholar
• Dolan ED, Moré JJ. Benchmarking optimization software with performance profiles. Math Program. 2002;91(2):201–213.
   Web of Science ®Google Scholar
• Bauschke HH, Combettes PL. Convex analysis and monotone operator theory in Hilbert spaces. 2nd ed. New York: Springer; 2017.
   Google Scholar
• Beck A, Guttmann-Beck N. FOM–a MATLAB toolbox of first-order methods for solving convex optimization problems. Optim Methods Softw. 2019;34(1):172–193.
   Web of Science ®Google Scholar
• Osilike MO, Aniagbosor SC. Weak and strong convergence theorems for fixed points of asymptotically nonexpansive mappings. Math Comput Model. 2000;32(10):1181–1191.
   Google Scholar
• Saejung S, Yotkaew P. Approximation of zeros of inverse strongly monotone operators in Banach spaces. Nonlinear Anal. 2012;75(2):742–750.
   Web of Science ®Google Scholar
• Denisov SV, Semenov VV, Chabak LM. Convergence of the modified extragradient method for variational inequalities with non-Lipschitz operators. Cybernet Syst Anal. 2015;51(5):757–765.
   Web of Science ®Google Scholar
• Tan B, Qin X, Yao JC. Strong convergence of inertial projection and contraction methods for pseudomonotone variational inequalities with applications to optimal control problems. J Global Optim. 2022;82(3):523–557.
   Web of Science ®Google Scholar
• Jolaoso LO, Taiwo A, Alakoya TO, et al. A strong convergence theorem for solving pseudo-monotone variational inequalities using projection methods. J Optim Theory Appl. 2020;185(3):744–766.
   Web of Science ®Google Scholar
• Hieu DV, Cho YJ, Xiao YB, et al. Modified extragradient method for pseudomonotone variational inequalities in infinite dimensional Hilbert spaces. Vietnam J Math. 2021;49(4):1165–1183.
   Web of Science ®Google Scholar
• Pietrus A, Scarinci T, Veliov VM. High order discrete approximations to Mayer's problems for linear systems. SIAM J Control Optim. 2018;56(1):102–119.
   Web of Science ®Google Scholar
• Bressan B, Piccoli B. Introduction to the mathematical theory of control. Springfield: American Institute of Mathematical Sciences (AIMS); 2007.
   Google Scholar