该文在约束集的线性化锥非空的条件下, 得到了带有等式和不等式约束的多目标规划问题的精确罚函数的存在性, 用原问题的二次近似在某些点上的Kuhn-Tucker乘子给出了罚因子的下界. 在此基础上, 利用极大熵方法的思想将罚函数转化为可微的无约束多目标规划问题并给出了求解该问题的一种交互式算法. 数值结果表明: 该文算法具有计算速度快、精度高、适用范围广且易于理解和使用等优点.

The existence of exact penalty function for multiobjective programming is proved under the condition that the linearized cone of constraints is nonempty, and the lower boundedness of penalty factor is obtained by using the Kuhn-Tucker multiplier of quadratic programming subproblem of the primal problem at some points. On this basis, an interactive algorithm is proposed by using the idea of maximum entropy method. Numerical experiments indicate that the algorithm is stable, efficient and easily used.