Tseng-type splitting projection algorithms for equilibrium problems in Hilbert spaces

References

• Blum E, Oettli W. From optimization and variational inequalities to equilibrium problems. Math Student. 1994;63:123–146.
   Google Scholar
• Muu LD, Oettli W. Convergence of an adaptive penalty scheme for finding constrained equilibria. Nonlinear Anal. 1992;18:1159–1166. doi: 10.1016/0362-546X(92)90159-C
   Web of Science ®Google Scholar
• Fan K. A minimax inequality and applications. In: Shisha O, editor. Inequalities, vol. III. New York: Academic Press; 1972. p. 103–113.
   Google Scholar
• Capătă A. On vector quasi-equilibrium problems via a Browder-type fixed-point theorem. Bull Malays Math Sci Soc. 2023;46(14). doi: 10.1007/s40840-022-01397-8
   Google Scholar
• Kassay G, Miholca M, Vinh NT. Vector quasi-equilibrium problems for the sum of two multivalued mappings. J Optim Theory Appl. 2016;169:424–442. doi: 10.1007/s10957-016-0919-9
   Web of Science ®Google Scholar
• Antipin AS. The convergence of proximal methods to fixed points of extremal mappings and estimates of their rate of convergence. Comp Math Math Phys. 1995;35:539–551.
   Web of Science ®Google Scholar
• Combettes PLHSA. Equilibrium programming in Hilbert spaces. J Nonlinear Convex Anal. 2005;6:117–136.
   Web of Science ®Google Scholar
• Dinh BV, Muu LD. A projection algorithm for solving pseudomonotone equilibrium problems and it's application to a class of bilevel equilibria. Optimization. 2015;64:1321–1328. doi: 10.1080/02331934.2013.864290
   Web of Science ®Google Scholar
• Iusem AN, Sosa W. Iterative algorithms for equilibrium problems. Optimization. 2003;52:301–316. doi: 10.1080/0233193031000120039
   Web of Science ®Google Scholar
• Khatibzadeh H, Mohebbi V. Proximal point algorithm for infinite pseudo-monotone bifunctions. Optimization. 2016;65:1629–1639. doi: 10.1080/02331934.2016.1153639
   Web of Science ®Google Scholar
• Tada A, Takahashi W. Weak and strong convergence theorems for a nonexpansive mapping and an equilibrium problem. J Optim Theory Appl. 2007;133:359–370. doi: 10.1007/s10957-007-9187-z
   Web of Science ®Google Scholar
• Quoc TD, Muu LD, Hien NV. Extragradient algorithms extended to equilibrium problems. Optimization. 2008;57:749–776. doi: 10.1080/02331930601122876
   Web of Science ®Google Scholar
• Santos PSM, Scheimberg S. An inexact subgradient algorithm for equilibrium problems. Comput Appl Math. 2011;30(1):91–107.
   Google Scholar
• Vuong PT, Strodiot JJ, Nguyen VH. Projected viscosity subgradient methods for variational inequalities with equilibrium problem constraints in Hilbert spaces. J Glob Optim. 2014;59:173–190. doi: 10.1007/s10898-013-0084-8
   Web of Science ®Google Scholar
• Pham KA, Trinh NH. Splitting extragradient-like algorithms for strongly pseudomonotone equilibrium problems. Numer Algor. 2017;76:67–91. doi: 10.1007/s11075-016-0244-2
   Web of Science ®Google Scholar
• Anh PK, Hai TN. A splitting algorithm for equilibrium problem given by the difference of two bifunctions. J Fixed Point Theory Appl. 2018;20(53). doi: 10.1007/s11784-018-0532-7
   Google Scholar
• Briceño-Arias LM. A Douglas–Rachford splitting method for solving equilibrium problems. Nonlinear Anal. 2012;75:6053–6059. doi: 10.1016/j.na.2012.06.014
   Web of Science ®Google Scholar
• Hai TN. Decomposition dynamical systems for solving variational inequalities. Optimization. 2023;72:883–903. doi: 10.1080/02331934.2021.1995732
   Web of Science ®Google Scholar
• Hai TN, Vinh NT. Two new splitting algorithms for equilibrium problems. Rev R Acad Cienc Exactas Fis Nat Ser A Mat. 2017;111:1051–1069. doi: 10.1007/s13398-016-0347-6
   Web of Science ®Google Scholar
• Hai TN, Thuong NT. A new splitting algorithm for equilibrium problems and applications. Stud Univ Babes-Bolyai Math. 2022;67:129–144. doi: 10.24193/subbmath
   Web of Science ®Google Scholar
• Hieu DV, Moudafi A. A barycentric projected-subgradient algorithm for equilibrium problems. J Nonlinear Var Anal. 2017;1:43–59.
   Google Scholar
• Moudafi A. On the convergence of splitting proximal methods for equilibrium problems in Hilbert spaces. J Math Anal Appl. 20009;359:508–513. doi: 10.1016/j.jmaa.2009.06.005
   Google Scholar
• Duc PM, Thanh LX. A splitting subgradient algorithm for solving equilibrium problems involving the sum of two bifunctions and application to Cournot-nash model. RAIRO-Oper Res. 2021;55:S1395–S1410. doi: 10.1051/ro/2020030
   Web of Science ®Google Scholar
• Korpelevich GM. An extragradient method for finding saddle points and for other problems. Ekonomika I Matematicheskie Metody. 1976;12:747–756.
   Google Scholar
• Santos PSM, Scheimberg S. A modified projection algorithm for constrained equilibrium problems. Optimization. 2017;66:2051–2062. doi: 10.1080/02331934.2016.1182528
   Web of Science ®Google Scholar
• Liu F, Nashed MZ. Regularization of nonlinear ill-posed variational inequalities and convergence rates. Set-Valued Anal. 1998;6:313–344. doi: 10.1023/A:1008643727926
   Google Scholar
• Alber YI, Iusem AN, Solodov MV. On the projected subgradient method for nonsmooth convex optimization in a Hilbert space. Math Program. 1998;81:23–35.
   Web of Science ®Google Scholar
• Maingé PE. Convergence theorems for inertial KM-type algorithms. J Comput Appl Math. 20008;219:223–236. doi: 10.1016/j.cam.2007.07.021
   Google Scholar
• Passty G. Ergodic convergence to a zero of the sum of monotone operators in Hilbert space. J Math Anal Appl. 1979;72:383–390. doi: 10.1016/0022-247X(79)90234-8
   Web of Science ®Google Scholar
• Anh PK, Vinh NT. Self-adaptive gradient projection algorithms for variational inequalities involving non-Lipschitz continuous operators. Numer Algor. 2019;81:983–1001. doi: 10.1007/s11075-018-0578-z
   Web of Science ®Google Scholar
• Tseng P. A modified forward-backward splitting method for maximal monotone mapping. SIAM J Control Optim. 2000;38:431–446. doi: 10.1137/S0363012998338806
   Web of Science ®Google Scholar
• Malitsky Y. Projected reflected gradient methods for monotone variational inequalities. SIAM J Optim. 2015;25:502–520. doi: 10.1137/14097238X
   Web of Science ®Google Scholar
• Solodov MV, Svaiter BF. A new projection method for monotone variational inequality problems. SIAM J Control Optim. 1999;37:765–776. doi: 10.1137/S0363012997317475
   Web of Science ®Google Scholar
• Contreras J, Klusch M, Krawczyk JB. Numerical solutions to Nash–Cournot equilibria in coupled constraint electricity markets. IEEE Tran Power Sys. 2004;19:195–206. doi: 10.1109/TPWRS.2003.820692
   Web of Science ®Google Scholar
• Quoc TD, Anh PN, Muu LD. Dual extragradient algorithms to equilibrium problems. J Glob Optim. 2012;52:139–159. doi: 10.1007/s10898-011-9693-2
   Web of Science ®Google Scholar
• Thuy LQ, Hai TN. A projected subgradient algorithm for bilevel equilibrium problems and applications. J Optim Theory Appl. 2017;175:411–431. doi: 10.1007/s10957-017-1176-2
   Web of Science ®Google Scholar