In order to generate properly efficient solutions of a general multiobjective optimization problem, a unified direction approach was introduced by Ghaznavi et al. (Optim. Methods Softw., 2019). However, there are some deficiencies in this work, and a counterexample is given to show that properly efficient solutions of a general multiobjective optimization problem cannot be obtained via optimal solutions of the proposed scalarized problem. In the present paper, by adding slack variables and surplus variables, we modify the direction scheme proposed by Ghaznavi et al. (Optim. Methods Softw., 2019), and achieve necessary and sufficient conditions for (weakly and properly) efficient solutions of a general multiobjective optimization problem via optimal solutions of the corresponding scalarized problem. Further, the efficiency of our method is demonstrated by numerical examples. This work fills some gaps in the work of Ghaznavi et al. (Optim. Methods Softw., 2019).

为了产生一般多目标优化问题的适当有效的解决方案，Ghaznavi等人引入了统一的方向方法。（Optim。Methods Softw。，2019）。但是，这项工作存在一些缺陷，并给出了一个反例以显示无法通过建议的标量问题的最优解获得一般多目标优化问题的适当有效解。在本文中，通过添加松弛变量和剩余变量，我们修改了Ghaznavi等人提出的方向方案。（Optim.Methods Softw。，2019），并通过相应标量问题的最优解为（多弱和适当）有效的解决一般多目标优化问题的有效条件提供了必要和充分的条件。更多，数值例子证明了我们方法的有效性。这项工作填补了Ghaznavi等人的工作中的一些空白。（Optim。Methods Softw。，2019）。