A Modified Alternated Inertial Subgradient Extragradient Algorithm for Solving Pseudo‐Monotone Variational Inequalities in Hilbert Spaces

This paper proposes an alternated inertial subgradient extragradient algorithm with a new variable stepsize rule for solving variational inequality problems in real Hilbert spaces. Unlike existing methods whose stepsize rules are fixed, open‐loop, or based only on the current residual, the proposed rule combines the current residual and the next‐step residual through a parameter . This yields a flexible trade‐off between the two residuals and ensures a positive lower bound for the stepsize sequence. Moreover, we obtain the R‐linear convergence results of our algorithm under the condition that the relevant mapping is strongly pseudo‐monotone. Numerical experiments demonstrate the effectiveness of the proposed method.