Optimal control of friction coefficient in Signorini contact problems

The optimal control of friction coefficient in Signorini contact problem is handled. First, we give the Tikhonov regularized optimal control problem subject to quasivariational inequality of the second kind. Since the relation control‐state is weak, we introduce another penalized control problem based algorithm of Bensoussan–Lions type applied to the quasi‐variational inequality. In order to get the optimality condition, and since the cost function is not differentiable, the quasi‐variational inequality is regularized to be a variational equality.