| 摘要: |
| 针对一类数据不确定的鲁棒凸多目标优化问题，提出了它在一般不确定集下的鲁棒对应形式;利用标量化方法将鲁棒多目标对应形式转化为鲁棒单目标凸优化问题，建立两者解集之间的联系;并得到了标量化鲁棒解的乘子刻画，及该标量化问题在其鲁棒解集上的一般化的常微分性质和常拉格朗日性质;最后通过前面的性质得到了鲁棒凸多目标优化问题的鲁棒G-真有效解集的刻画并加以证明. |
| 关键词: 多目标优化 标量化 鲁棒真有效解集 |
| DOI： |
| 分类号: |
| 基金项目: |
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| Optimality and Duality for Robust Multiobjective Optimization Problems |
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ZHENG Shuang，ZHOU Jun-yi
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| Abstract: |
| For a class of robust convex multiobjective optimization problem with uncertain data，a robust counterpart under general uncertain sets is given. The scalar quantization method is used to transform the robust multiobjective counterpart into a robust single object convex optimization problem，to establish the connection between the two solutions. And we obtain a multiplicative description of a scalarized robust solution and the generalized constant differential property and constant Lagrangian property of the scalarization problem on its robust solution set. Finally，through the preceding properties，the proper efficient solution set of a robust convex multiobjective optimization problem is characterized and proved. |
| Key words: multiobjective optimization scalarization robust proper efficient solution set |
