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The subgradient extragradient method extended to pseudomonotone equilibrium problems and fixed point problems in Hilbert space. (English) Zbl 1459.90222

Summary: In this paper, we first introduce and analyze a new algorithm for solving equilibrium problems involving Lipschitz-type and pseudomonotone bifunctions in real Hilbert space. The algorithm uses a new step size, we prove the iterative sequence generated by the algorithm converge strongly to a common solution of equilibrium problem and a fixed point problem without the knowledge of the Lipschitz-type constants of bifunction. Finally, another similar algorithm is proposed and numerical experiments are reported to illustrate the efficiency of the proposed algorithms.

MSC:

90C48 Programming in abstract spaces
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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