A new approach via the subgradient extragradient method to solving pseudomonotone equilibrium problems in Hilbert spaces
Simeon Reich, Duong Viet Thong, Olaniyi S. Iyiola, Yekini Shehu, Nguyen Ngoc Duong · Optimization · 2025
In this work, we propose and analyze a new algorithm for solving equilibrium problems with pseudomonotone and Lipschitz-type bifunctions in a real Hilbert space. The main theoretical contribution is proving the strong convergence of the algorithm to a solution without knowing the Lipschitz constants a priori. This expands the applicability of the method to problems. Additionally, we derive the convergence rate under extra assumptions of strong pseudomonotonicity and Lipschitz continuity. Numerical experiments on equilibrium problems demonstrate that the proposed algorithm is efficient and robust. It performs well even without precise knowledge of the Lipschitz constants. This illustrates the practical advantages of the proposed technique for finding equilibrium solutions.