New extragradient method for a class of equilibrium problems in Hilbert spaces

References

• Blum E , Oettli W . From optimization and variational inequalities to equilibrium problems. Math Program. 1994;63:123–145.
   Google Scholar
• Daniele P , Giannessi F , Maugeri A . Equilibrium problems and variational models. Dordrecht: Kluwer; 2003.
   Google Scholar
• Facchinei F , Pang JS . Finite-dimensional variational inequalities and complementarity problems. Berlin: Springer; 2002.
   Google Scholar
• Moudafi A . Proximal point algorithm extended to equilibrium problem. J Nat Geometry. 1999;15:91–100.
   Google Scholar
• Konnov IV . Partial proximal point method for nonmonotone equilibrium problems. Optim Meth Software. 2006;21:373–384.
   Web of Science ®Google Scholar
• Iusem AN , Sosa W . On the proximal point method for equilibrium problems in Hilbert spaces. Optimization. 2010;59:1259–1274.
   Web of Science ®Google Scholar
• Combettes PL , Hirstoaga SA . Equilibrium programming in Hilbert spaces. J Nonlinear Convex Anal. 2005;6:117–136.
   Web of Science ®Google Scholar
• Mastroeni G . On auxiliary principle for equilibrium problems. Publicatione del Dipartimento di Mathematica dell, Universita di Pisa. 2000;3:1244–1258.
   Google Scholar
• Mastroeni G . Gap function for equilibrium problems. J Global Optim. 2003;27:411–426.
   Web of Science ®Google Scholar
• Konnov IV . Regularized penalty method for general equilibrium problems in Banach spaces. J Optim Theory Appl. 2015;164:500–513.
   Web of Science ®Google Scholar
• Iusem AN , Sosa W . Iterative algorithms for equilibrium problems. Optimization. 2003;52:301–316.
   Web of Science ®Google Scholar
• Ceng LC , Latifc A , Al-Mazrooeid AE . Hybrid viscosity methods for equilibrium problems, variational inequalities, and fixed point problems. Appl Anal. 2016;95:1088–1117.
   Web of Science ®Google Scholar
• Hieu DV . Parallel hybrid methods for generalized equilibrium problems and asymptotically strictly pseudocontractive mappings. J Appl Math Comput. 2017;53:531–554. DOI:10.1007/s12190-015-0980-9
   Web of Science ®Google Scholar
• Yao Y , Chen R , Xu HK . Schemes for finding minimum-norm solutions of variational inequalities. Nonlinear Anal. 2010;72:3447–3456.
   Web of Science ®Google Scholar
• Yao Y , Liou YC , Kang SM . Approach to common elements of variational inequality problems and fixed point problems via a relaxed extragradient method. Comput Math Appl. 2010;59:3472–3480.
   Web of Science ®Google Scholar
• Yao Y , Noor MA , Liou YC . Strong convergence of a modified extragradient method to the minimum-norm solution of variational inequalities. Abstr Appl Anal. 2012;2012:ID 817436, 9p.
   Google Scholar
• Yao Y , Postolache M , Liou YC , et al . Construction algorithms for a class of monotone variational inequalities. Optim Lett. 2016;10:1519–1528.
   Web of Science ®Google Scholar
• Zegeye H , Shahzad N , Yao Y . Minimum-norm solution of variational inequality and fixed point problem in Banach spaces. Optimization. 2015;64:453–471.
   Web of Science ®Google Scholar
• Yao Y , Liou YC , Yao JC . Convergence theorem for equilibrium problems and fixed point problems of infinite family of nonexpansive mappings. Fixed Point Theory Appl. 2007;2007:ID 64363, 12p.
   Google Scholar
• Cohen G . Auxiliary problem principle and decomposition of optimization problems. J Optim Theory Appl. 1980;32:277–305.
   Web of Science ®Google Scholar
• Cohen G . Auxiliary principle extended to variational inequalities. J Optim Theory Appl. 1988;59:325–333.
   Web of Science ®Google Scholar
• Flam SD , Antipin AS . Equilibrium programming and proximal-like algorithms. Math Program. 1997;78:29–41.
   Web of Science ®Google Scholar
• Quoc TD , Muu LD , Hien NV . Extragradient algorithms extended to equilibrium problems. Optimization. 2008;57:749–776.
   Web of Science ®Google Scholar
• Korpelevich GM . The extragradient method for finding saddle points and other problems. Ekonomika i Matematicheskie Metody. 1976;12:747–756.
   Google Scholar
• Vuong PT , Strodiot JJ , Nguyen VH . On extragradient-viscosity methods for solving equilibrium and fixed point problems in a Hilbert space. Optimization. 2015;64:429–451.
   Web of Science ®Google Scholar
• Hieu DV . Parallel extragradient-proximal methods for split equilibrium problems. Math Model Anal. 2016;21:478–501.
   Web of Science ®Google Scholar
• Hieu DV , Muu LD , Anh PK . Parallel hybrid extragradient methods for pseudomonotone equilibrium problems and nonexpansive mappings. Numer Algorithms. 2016;73:197–217. DOI:10.1007/s11075-015-0092-5
   Web of Science ®Google Scholar
• Hieu DV , Anh PK , Muu LD . Modified hybrid projection methods for finding common solutions to variational inequality problems. Comput Optim Appl. 2017;66:75–96. DOI:10.1007/s10589-016-9857-6
   Web of Science ®Google Scholar
• Hieu DV . An extension of hybrid method without extrapolation step to equilibrium problems. J Ind Manag Optim. 2016. DOI:10.3934/jimo.2017015
   Web of Science ®Google Scholar
• Strodiot JJ , Nguyen TTV , Nguyen VH . A new class of hybrid extragradient algorithms for solving quasi-equilibrium problems. J Glob Optim. 2013;56:373–397.
   Web of Science ®Google Scholar
• Strodiot JJ , Vuong PT , Nguyen TTV . A class of shrinking projection extragradient methods for solving non-monotone equilibrium problems in Hilbert spaces. J Glob Optim. 2016;64:159–178.
   Web of Science ®Google Scholar
• Bianchi M , Schaible S . Generalized monotone bifunctions and equilibrium problems. J Optim Theory Appl. 1996;90:31–43.
   Web of Science ®Google Scholar
• Muu LD , Oettli W . Convergence of an adative penalty scheme for finding constrained equilibria. Nonlinear Anal TMA. 1992;18:1159–1166.
   Web of Science ®Google Scholar
• Muu LD , Quy NV . On existence and solution methods for strongly pseudomonotone equilibrium problems. Vietnam J Math. 2015;43:229–238.
   Web of Science ®Google Scholar
• Tiel JV . Convex analysis. New York (NY): Wiley; 1984.
   Google Scholar
• Rudin W . Real and complex analysis. 3rd ed. New York (NY): McGraw-Hill; 1987.
   Google Scholar
• Khanh PD . A new extragradient method for strongly pseudomonotone variational inequalities. Numer Funct Anal Optim. 2016;37:1131–1143. DOI:10.1080/01630563.2016.1212372
   Web of Science ®Google Scholar
• Iusem AN , Svaiter BF . A variant of Korpelevich’s method for variational inequalities with a new search strategy. Optimization. 1997;42:309–321.
   Google Scholar