一类非可微多目标规划的改进的Mond-Weir型对偶

The Improved Mond-Weir Duality for a Class of Nondifferentiable Multiobjective Programming

【目的】研究一类非可微多目标规划问题改进的Mond-Weir型对偶。【方法】分析Mond-Weir型对偶问题基础上,给出该问题的一类改进的Mond-Weir型对偶模型,利用G-不变凸性证明原问题与对偶问题之间的对偶结果。【结果】在适当条件下,得出该问题与对偶问题的弱对偶定理、强对偶定理和非极大逆对偶定理并进行证明。【结论】改进的MondWeir型对偶结果可以在更弱的条件下得以证明。

[Purposes]The improved Mond-Weir type dual problem of a class of nondifferentiable multiobjective programs were studied.[Methods]The improved Mond-Weir type dual problem is formulated.G-invex assumption were used to establish duality theorems relating the problem and the dual problems which based on the analysis of Mond-Weir type dual problem.[Findings]Weak duality theorems,strong duality theorem and no-maximal converse duality theorem were established under suitable conditions.[Conclusions]The improved Mond-Weir duality results were proved under weaker assumptions.