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For solving pseudo-monotone variational inequality problems in Hilbert spaces, we introduce a new algorithm with self-adaptive technique. The algorithm is based on the projection method and inertial method. The strong convergence theorem is established under some appropriate conditions. Finally, we provide some numerical experiments to illustrate the effectiveness and advantages of the proposed algorithm.

Inertial modified projection algorithm with self-adaptive technique for solving pseudo-monotone variational inequality problems in Hilbert spaces