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.
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.
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.
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.
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.
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.
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