对偶理论是数学规划的理论基础，其中在各种约束条件下对弱对偶定理的研究是对偶理论研究的重要组成部分。
The duality theory is the basic theory for mathematical planning in which the study of weak duality theorem under different controlling conditions is an important part of duality theorem research.
接着，利用函数的上次微分构造了不可微向量优化问题（VP）的广义对偶模型，并且在适当的弱凸性条件下建立了弱对偶定理。
Finally, the generalized dual model of the problem (VP) is presented with the help of upper subdifferential of function, and a weak duality theorem is given.
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