The main goal of this article is to study a general augmented Lagrangian method for optimal control problems governed by mixed (quasi-)equilibrium problems. We establish zero duality gap properties between a primal problem and its augmented Lagrangian dual problem. As a consequence, we give some existence results for optimal control problem governed by evolutionary quasi-variational inequalities. An application to optimal control of obstacle problems described by quasi-hemivariational inequalities is studied. The results obtained in this article are new and improves considerably many recent results in literature.

中文翻译：

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由应用混合准平衡问题控制的最优控制问题的增广拉格朗日方法

本文的主要目标是研究由混合（准）平衡问题控制的最优控制问题的一般增广拉格朗日方法。我们在原始问题和它的增广拉格朗日对偶问题之间建立零对偶间隙属性。因此，我们给出了由进化拟变分不等式支配的最优控制问题的一些存在性结果。研究了由拟半变分不等式描述的障碍问题优化控制的应用。在这篇文章中获得的结果是新的，并且大大改进了文献中的许多最近的结果。