We consider multiobjective optimal control problems for semilinear parabolic systems subject to pointwise state constraints, integral state-control constraints and pointwise state-control constraints. In addition, the data of the problems need not be twice Fréchet differentiable. Employing the second-order directional derivative (in the sense of Demyanov-Pevnyi) for the involved functions, we establish necessary optimality conditions, via second-order Lagrange multiplier rules of Fritz-John type, for local weak Pareto solutions of the problems.

中文翻译：

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半线性抛物方程的多目标最优控制中的二阶拉格朗日乘数规则

我们考虑半线性抛物系统的多目标最优控制问题，这些问题受点状状态约束，积分状态控制约束和点状状态控制约束的约束。另外，问题的数据不需要两次弗雷歇特可区分。对于所涉及的函数，采用二阶有向导数（在Demyanov-Pevnyi的意义上），我们通过Fritz-John型的二阶Lagrange乘数规则为问题的局部弱Pareto解建立了必要的最优性条件。