We show in this work the zero duality gap property for an optimal control problem governed by a multivalued hemivariational inequality with unbounded constraint set. Based on the existence of solutions to the inequality, we establish several sufficient conditions for the zero duality gap property between the optimal control problem and its nonlinear dual problem by using nonlinear Lagrangian methods. Moreover, we obtain a convergence result for the optimal control problem governed by a perturbed multivalued hemivariational inequality.

中文翻译：

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多值半变分不等式控制的最优控制问题的零对偶间隙性质

我们在这项工作中显示了由无限制约束集的多值半变分不等性控制的最优控制问题的零对偶间隙属性。基于不等式解的存在性，我们使用非线性拉格朗日方法为最优控制问题与其非线性对偶问题之间的零对偶间隙性质建立了几个充分条件。此外，我们获得了由扰动的多值半变分不等式控制的最优控制问题的收敛结果。