并且证明了拉格朗日对偶界与通过凸松弛得到的下界是相等的；

We prove that the Lagrangian dual bound is identical to the lower bound obtained by convex relaxation.

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推广了对偶的概念与对偶原理的思想，在格论中引入了对偶律，并讨论了与之相关的一些概念和性质。

The dual law in lattice theory is introduced and some concepts and properties relative to it are discussed, while generalizing the concept of duality and the idea of the duality principle.

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首先讨论了格的子集生成幻和生成对偶幻的运算性质。

This paper discusses the operational properties of generated ideals and generated dual ideals.

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