Robust Subgradient Extragradient Methods With Increasing Step‐Size Rules for Equilibrium Problems

ABSTRACT We propose two modified subgradient extragradient methods for solving equilibrium problems associated with pseudomonotone bifunctions of Lipschitz type in real Hilbert spaces. The principal novelty of the proposed algorithms lies in an increasing self‐adaptive step‐size rule , updated via a simple recursive procedure. This strategy removes the requirement for prior knowledge of the Lipschitz constants of the bifunction, thereby enhancing the applicability of the methods to large‐scale and ill‐conditioned problems. Under standard assumptions, we establish both weak and strong convergence of the proposed methods, extending and improving several existing results in the literature. Finally, numerical experiments are presented to demonstrate the computational efficiency and practical performance of the algorithms.