Two new splitting algorithms for equilibrium problems

A splitting algorithm for finding fixed points of nonexpansive mappings and solving equilibrium problems

“…since { x k − x * } is convergent, γ ∈ (0, 1), and β k → 0 as k → ∞. To the end, by (13) and (14), we obtain…”

“…In order to reduce the computational cost, several splitting algorithms have been developed for some classes of maximal monotone operator inclusion, variational inequality, and equilibrium problems (see e.g. [1,8,9,11,13,14,21,26,36]).…”

“…• Convergence of the proposed algorithms is ensured without any Lipschitz type or Hölder conditions that are required in some existing splitting algorithms for equilibrium problems (e.g. in [1,13]).…”

A splitting subgradient algorithm for solving equilibrium problems involving the sum of two bifunctions and application to cournot-nash model

“…At each iteration of the algorithm, two strongly convex subprograms are required to solve separately, one for each component bifunction. In contrast to the splitting algorithms previously proposed in [1,11], our algorithm is convergent for paramonotone and strongly pseudomonotone bifunctions without any Lipschitz type as well as Hölder continuity condition of the bifunctions involved. Furthermore, we show that the ergodic sequence defined by the algorithm iterates converges to a solution without paramonotonicity property.…”

“…In another direction, also for the sake of reducing computational cost, some splitting algorithms have been developed (see e.g. [1,11,18]) for monotone equilibrium problems where the bifunction f can be decomposed into the sum of two bifunctions. In these algorithms the convex subprograms (resp.…”