This paper deals with second-order necessary and sufficient optimality conditions of Karush–Kuhn–Tucker-type for local optimal solutions in the sense of Pareto to a class of multi-objective discrete optimal control problems with nonconvex cost functions and state-control constraints. By establishing an abstract result on second-order optimality conditions for a multi-objective mathematical programming problem, we derive second-order necessary and sufficient optimality conditions for a multi-objective discrete optimal control problem. Using a common critical cone for both the second-order necessary and sufficient optimality conditions, we obtain “no-gap” between second-order optimality conditions.

本文针对一类具有非凸成本函数和状态控制约束的多目标离散最优控制问题，从帕累托的意义上讨论了Karush–Kuhn–Tucker型局部最优解的二阶充要条件。通过建立多目标数学规划问题的二阶最优条件的抽象结果，我们得出了多目标离散最优控制问题的二阶必要和充分的最优条件。对第二阶必要条件和足够的最优条件都使用一个共同的临界锥，我们在第二阶最优条件之间获得了“无间隙”。