基于~Pascoletti-Serafini~标量化方法, 利用罚函数思想提出了一类新的标量化函数, 进而获得非凸多目标优化问题真有效解的充分条件和必要条件. 该结果的建立不需要目标函数的像集有界这一条件, 故文章是对~Akbari~等人[J. Optim. Theory Appl., 2018, 178(2): 560--590]建立的相应标量化结果的改进.

In this paper, based on the Pascoletti-Serafini scalarization method, a new class of scalarized function is proposed via a penalty function approach. Then we achieve necessary and sufficient conditions for properly efficient solutions to nonconvex multiobjective optimization problem without the boundedness assumption of the image under the objective function. These results improve the corresponding work of Akbari, et al. [J. Optim. Theory Appl., 2018, 178(2): 560--590].