对偶定理是一个数学术语，指的是若两逻辑式相等，则它们的对偶式也相等。 对偶式指的是对于任何一个逻辑式Y，若将其中的“·”换成“+”，“+”换成“·”，0换成1，1换成0，则得到一个新的逻辑式Y'，Y'就是Y的对偶式。显然Y和Y'互为对偶式。
Based on these, Vector-valued lagrange duality of vector extremum problems are established, including weak duality,strong duality and convex duality theorem in linear space.
在此基础上,给出了向量值优化问题的向量值Lagrange对偶,其中包括弱对偶定理、强对偶定理和逆对偶定理。
参考来源 - 抽象空间中向量极值问题的最优性条件和Lagrange对偶·2,447,543篇论文数据，部分数据来源于NoteExpress
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.
线性规划中对偶理论的一系列定理是针对变量无上界的线性规划的。
In linear programming, a series of theorems of dual theory are adopted to deal with the linear programmings with unbounded variables.
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