Abstract
In this paper, we construct an implementable augmented Lagrangian method to solve second-order cone constrained variational inequalities (SOCCVI) problem. By considering a special optimization problem that has the same solution as the SOCCVI problem, we obtain different equivalent transformation forms of the SOCCVI problem. Using the equivalent transformation forms and the properties of the projection operators, the augmented Lagrangian method can be established and its global convergence is proved. The inexact Newton method is used to solve the inner problems which arise from the augmented Lagrangian method for solving the numerical examples. Numerical results for three examples are reported to verify the effectiveness of the augmented Lagrangian method for obtaining approximate solutions.
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