Modified Goldstein–Levitin–Polyak Projection Method for Asymmetric Strongly Monotone Variational Inequalities

In this paper, we present a modified Goldstein–Levitin–Polyak projection method for asymmetric strongly monotone variational inequality problems. A practical and robust stepsize choice strategy, termed self-adaptive procedure, is developed. The global convergence of the resulting algorithm is established under the same conditions used in the original projection method. Numerical results and comparison with some existing projection-type methods are given to illustrate the efficiency of the proposed method.

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