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.
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.
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.
给出了格蕴涵代数、MV代数、R 0代数等一些格上蕴涵代数之间的关系，并建立了它们的对偶代数。
This paper gives out that the relationship among lattice implication algebras, MV algebras, R0 algebras and other implication algebras based on lattices, and their dual algebras are established.
然后，运用凸优化技术分析了该资源分配问题，并基于拉格朗日对偶法给出了一种子载波和功率最优分配算法。
Then, by use of multiple carrier system's frequency-sharing property and convex optimization, a subcarrier and power optimal allocation algorithm is proposed based on Lagrangian duality theory.
采用椭球剖分策略剖分可行域为小的椭球，用投影次梯度算法解松弛二次规划问题的拉格朗日对偶问题，从而获得原问题的一个下界。
A projection subgradient algorithm for the Lagrangian dual problem of the relaxed quadratic problem is employed to general lower bounds of the optimal value for the original problem.
针对问题的非凸性，提出了基于拉格朗日对偶方法的最优子信道、速率和功率分配算法，并从经济学的角度予以解释。
We formulated this optimization problem and solved it using the Lagrangian dual method and interpreted it from the angle of economics.
从自适应控制算法与参数估计算法的对偶性出发，提出了自适应控制算法的一种统一格式。
A new unity pattern of the adaptive control algorithm is introduced with the standpoint of the duality between adaptive control algorithm and parameter estimation.
对最适化条件、拉格朗日乘数理论以及对偶理论的综合论述，以及在控制、通信、动力系统和资源分配问题上的应用。
Comprehensive treatment of optimality conditions, Lagrange multiplier theory, and duality theory. Applications drawn from control, communications, power systems, and resource allocation problems.
提出了一个新的支持向量机模型——基于边界调节的支持向量机，并利用拉格朗日定理得到了这种支持向量机的对偶目标函数。
In order for an SVM to be more robust to noise, a new SVM model i. e., the support vector machine based on adjustive boundary SVMAB is proposed.
变精度对偶概念格的概念数量远远少于模糊对偶概念格的概念数。
The results show that the number of concepts in variable threshold dual concept lattices is less than that in fuzzy dual concept lattices, and the important concepts are preserved.
变精度对偶概念格的概念数量远远少于模糊对偶概念格的概念数。
The results show that the number of concepts in variable threshold dual concept lattices is less than that in fuzzy dual concept lattices, and the important concepts are preserved.
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