Abstract
A self-adaptive alternating direction method of multipliers was proposed for the approximation solution of variational inequalities with biharmonic operators and curvature obstacle. An augmented Lagrange functional was introduced with an auxiliary variable to express the curvature function, and a constrained minimization problem equivalent to a saddle-point one was deduced. Then the alternating direction method of multipliers was applied to solve the saddle-point problem. By means of the balance principle and iterative functions, a self-adaptive rule was obtained to adjust the penalty parameter automatically, and improve the computation efficiency. The convergence of this method was proved and the penalty parameter approximation was given in detail with the iterative functions. The numerical results illustrate the effectiveness of the proposed method.
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