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.
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.
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.
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.
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