[PDF] Top 20 Proximal algorithms for a class of mixed equilibrium problems

... Throughout the paper, H is a real Hilbert space with inner product · , · and induced norm · . Let K be a nonempty closed convex subset of H, F : K × K → R be a bifunction and ϕ : K → R ∪ {+∞} be a proper generalized real ... See full document

... wide class of obstacle, unilateral, free, moving, equilibrium ...point problems, the origin of which can be traced back to Lions and Stampacchia ...iterative algorithms in the literature for ... See full document

... the class of κ-strictly pseudocontractive includes the class of nonexpansive mappings as a special ...The class of κ-strictly pseudocontractive mappings was intro- duced by Browder and Petryshyn ... See full document

... wide class of obstacle, unilateral, free, moving, equilibrium ...iterative algorithms in the literature for finding approximate solutions of VIP ... See full document

... It should be pointed out that the class of δ-pseudo-contractive (resp. pseudo- contractive, i.e., δ = 1 in (ii)) mappings is larger that of δ-Lipschitz continuous (resp. nonexpansive, i.e., Lipschitz continuous ... See full document

... point problems, complementarity problems, opti- mization problems, Nash equilibrium problems in noncooperative games, etc (see ...several problems arising in several areas of ... See full document

... hybrid proximal-type algorithms are established; that is, under appropriate conditions, the sequences generated by these various algorithms converge strongly to the same point in EP ∩ FS ∩ T −1 ... See full document

... hybrid proximal-point algorithms for finding a common element of the zero point of a maximal monotone operator, the set of solutions of equilibrium problems, and the set of solution of the ... See full document

... and proximal and resolvent equations techniques cannot be extended and generalized to suggest and analyze similar iterative methods for solving invex equilibrium problems and variational-like ... See full document

... point problems, variational inequality problems, minimization problems, optimization problems, variational inequality problems, vector equilibrium problems, Nash ... See full document

... eralized mixed equilibrium problems, variational inclusion problems and a finite family of quasi-nonexpansive mappings,” Journal of Inequalities and Applications, ... See full document

... Equilibrium problems theory provides us with a unified, natural, novel and general frame- work to study a wide class of problems, which arise in finance, economics, network anal- ysis, ... See full document

... The class of quasi-φ -nonexpansive mappings and the class of asymptotically quasi-φ -nonexpansive mappings are more general than the class of relatively nonexpan- sive mappings and the class ... See full document

... For each fixed vector of weights r this variational inequality admits a unique solution e R , (since F r is strictly monotone), which is the norma ed Rosen ui- librium corresponding to the given weight. For the eco- ... See full document

... wide class of problems arising in many fields and yet solution algorithms are extremely ...Nash equilibrium problem as a mathematical program with complementarity constraints ... See full document

... Iterative algorithms have emerged as an effective and powerful tool for studying a wide class of problems which arise in economics, finance, image reconstruction, ecology, trans- portation, network, ... See full document

... a mixed equilibrium problem (MEP) and the set of common fixed points of finitely many nonexpansive mappings in a real Hilbert ...hybrid algorithms for finding a common fixed point of a nonexpansive ... See full document

... extragradient algorithms for finding a solution of the problem ...the proximal method. However, the problems of solving strongly convex optimization subproblems and of finding shrinking projections in ... See full document

... This paper focuses mainly on a split equilibrium problem and nonexpansive mapping involving pseudomonotone and monotone equilibrium bifunctions in real Hilbert spaces. In detail, let f : C × C → R be a ... See full document

... 36. Wittmann, R: Approximation of fixed points of non-expansive mappings. Arch. Math. 58, 486-491 (1992) 37. Moudafi, A: Viscosity approximation methods for fixed-points problems. J. Math. Anal. Appl. 241, 46-55 ... See full document