一类广义凸多目标变分问题的对偶模型的几个补充定理

The Additional Theorems of a Duality for a Class of Generalized Convex Multiobjective Variational Problems

考虑一类约束多目标变分问题 ,在〔8〕的基础上 ,目标函数和约束函数的广义 (F ,ρ) -凸性假设下 ,证明了原问题和对偶问题关于有效解的几个弱对偶定理和强对偶定理 .推广了这一领域里最近一些文献中的相应模型与结果 .同时推广了〔8〕的结果 .

A class of constrained multiobjective variational problems are considered.On the basic of 〔8〕,under generalized (F,ρ)-convexity assumptions on the objective and the constraint functions,a number of weak and strong duality theorems are proved to relate efficient solutions for primal and dual problems.The results given in this paper generalized the corresponding some recent papers in this field,Also improved the results of 〔8〕.