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.

中文翻译：

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Signorini接触问题中摩擦系数的优化控制

处理了Signorini接触问题中摩擦系数的最优控制。首先，我们给出服从第二类拟变分不等式的Tikhonov 正则化最优控制问题。由于关系控制状态较弱，我们引入了另一种基于惩罚控制问题的 Bensoussan 算法——Lions 类型应用于拟变分不等式。为了得到最优条件，并且由于代价函数不可微，拟变分不等式被正则化为变分等式。