MODIFIED INERTIAL SUBGRADIENT EXTRAGRADIENT ALGORITHM WITH SELF-ADAPTIVE STEP SIZES FOR SOLVING SPLIT EQUILIBRIUM PROBLEMS

K. RATTANASEEHA; M. KHONCHALIEW

MODIFIED INERTIAL SUBGRADIENT EXTRAGRADIENT ALGORITHM WITH SELF-ADAPTIVE STEP SIZES FOR SOLVING SPLIT EQUILIBRIUM PROBLEMS

Authors

K. RATTANASEEHA Faculty of Science and Technology, Loei Rajabhat University, Loei, THAILAND
M. KHONCHALIEW Department of Mathematics, Faculty of Science, Lampang Rajabhat University, Lampang 52100, Thailand

Keywords:

split equilibrium problems, pseudomonotone bifunction, inertial method, subgradient extragradient method

Abstract

In this paper, we introduce a modified inertial subgradient extragradient algorithm featuring self-adaptive step sizes. Our focus is on solving split equilibrium problems that involve pseudomonotone bifunctions satisfying Lipschitz-type continuity within real Hilbert spaces. We demonstrate a strong convergence theorem for the proposed algorithm, requiring neither prior knowledge of the operator norm of the bounded linear operator nor the Lipschitz constants of bifunctions. This convergence holds under certain constraint qualifications of the scalar sequences.